What is Dx: Definition and 306 Discussions
The Nikon DX format is an alternative name used by Nikon corporation for APS-C image sensor format being approximately 24x16 mm. Its dimensions are about 2⁄3 (29 mm vs 43 mm diagonal, approx.) those of the 35mm format. The format was created by Nikon for its digital SLR cameras, many of which are equipped with DX-sized sensors. DX format is very similar in size to sensors from Pentax, Sony and other camera manufacturers. All are referred to as APS-C, including the Canon cameras with a slightly smaller sensor.
Nikon has produced 23 lenses for the DX format, from macro to telephoto lenses. 35mm format lenses can also be used with DX format cameras, with additional advantages: less vignetting, less distortion and often better border sharpness. Disadvantages of 35mm lenses include generally higher weight and incompatible features such as autofocus with some lower-end DX cameras. Nikon has also produced digital SLRs that feature the larger Nikon FX format sensor that is the size of the 135 film format.
In 2013, Nikon introduced a high-end compact camera with a DX-sized sensor, the Nikon Coolpix A, featuring an 18.5 mm lens.
View More On Wikipedia.org
Nikon has produced 23 lenses for the DX format, from macro to telephoto lenses. 35mm format lenses can also be used with DX format cameras, with additional advantages: less vignetting, less distortion and often better border sharpness. Disadvantages of 35mm lenses include generally higher weight and incompatible features such as autofocus with some lower-end DX cameras. Nikon has also produced digital SLRs that feature the larger Nikon FX format sensor that is the size of the 135 film format.
In 2013, Nikon introduced a high-end compact camera with a DX-sized sensor, the Nikon Coolpix A, featuring an 18.5 mm lens.
View More On Wikipedia.org
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MHB Integrating e^X - e^-x/e^-x+1 dx
how do you integrate e^X-e^-x/e^-x+1 dx i am trying multiplying by e^x and trying to make it into no fraction but i am having no luck- markosheehan
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- Dx E^x Integrating
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- Forum: Calculus
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MHB 242.8.2.8 int x sin (x/5) dx. IBP
$\large{242.8.2.8}$ $\displaystyle I_8=\int(x)\sin{\left(\frac{x}{5}\right)} \, dx= 25\sin\left(\dfrac{x}{5}\right)-5\cos\left(\dfrac{x}{5}\right)x$ $$\begin{align} u&=\frac{x}{5} &5du&=dx &x&=5u \\ \end{align}\\ $$ thus $\displaystyle I_8=25\int u\sin{u} \, du$ IBP $$\begin{align} u_1&=u... -
I What is the difference between dx, Δx and δx?
What is the difference between dx, Δx and δx? Δ = difference d = Δ but small difference, infinitesimal δ = d but along a curve Mathematical symbols are always graphics.I’m not sure if that will be true, but it would be beautiful.- Consolacion Ruiz
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- Difference Dx
- Replies: 5
- Forum: Calculus
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MHB Thanks! Glad you found it helpful.
Whitman 8.3.12 $$\int \frac{{x}^{3 }}{\sqrt{4x ^2 - 1}} \ dx = \frac{\left(2{x}^{2}+1\right)\sqrt{4{x}^{2}-1}}{24}$$ $$u=4x^2 - 1 \ \ \ \ du=8x \ dx \ \ \ x=\left(\frac{u-1}{4 }\right)^\frac{1}{2}$$ Substitute and simplify $$\frac{1}{32}\displaystyle \int\dfrac{u+1}{\sqrt{u}}\,\mathrm{d}u$$ -
MHB -w8.3.11 int sqrt{x} dx sqrt{1-x}
w8.3.11 nmh{1000} $\displaystyle I= \int\frac {\sqrt{x}} {\sqrt{1-x}}\ dx=\arcsin\left({\sqrt{x}}\right)-\sqrt{x}\sqrt{1 - x}+C $ Substitutions $x=\sin^2 \left({u}\right) \quad dx=2\sin\left({u}\right) \cos\left({u}\right) \ du \quad u=\arcsin\left({\sqrt{x}}\right)$ This evaluates to... -
MHB -w8.3.9 int 1/(x^2 (1+x^2)) dx
Whitman 8.3.9 $$\displaystyle \int\frac{1 }{{x}^{2}\left(1+{x}^{2}\right)} \ dx =-\arctan\left({x}\right)-\frac{1}{x}+C $$ Expand $$\displaystyle \int\frac{1}{{x}^{2}}\ dx -\int \frac{1}{{x}^{2}+1}dx $$ Solving $$\displaystyle \int\frac{1}{{x}^{2}}\ dx =-\frac{1}{x}+C$$ Solving... -
MHB How can I use integration by parts to solve $\displaystyle \int\sin^2(x) \ dx$?
mnt{w.8.4.5} nmh{1000} $\displaystyle \int\sin^2 \left({x}\right) \ dx = \frac{x}{2}-\frac{\sin\left({2x }\right)}{4}+C $ As given by a table reference Integral calculator uses reduction formula to solve this But this is an exercise following integration by parts so.. $\displaystyle \int\sin^2... -
MHB 8.4.2 - Computing ∫ x² cos(x) dx
8.4.2 $$\int {x}^{2}\cos\left({x}\right)\ dx = {x}^{2}\sin\left({x}\right) -2\sin\left({x}\right) +2x\cos\left({x}\right) + C $$ $$uv-\int v \ du $$ $$u={x}^{2}\ \ \ dv=\cos\left({x}\right)\ dx $$ $$du=2x \ dx \ \ \ \ v=\sin\left({x}\right)$$... -
MHB W8.3.6 int x^2 sqrt(1-x^2) dx
W8.3.6 evaluate $$\int {x}^{2}\sqrt{1-{x}^{2 }} \ dx = \arcsin\left({x}\right)/8—\sin\left({4\arcsin\left({x}\right)}\right)/32 + C $$ This is from an exercise on trig substitutions so $$x=\sin\left({x}\right) \text{ so } \int\sin^2 \left({x}\right)\sqrt{1-\sin^2 \left({x}\right)}\ dx... -
MHB What is the integral of $\sqrt{x^2-1}$? What is the integral of $\sqrt{x^2-1}$?
Evaluate $$\displaystyle \int\sqrt{{x}^{2}-1} \ dx$$ First the indenitly of $\tan^2 \left({x}\right)=\sec^2 \left({x}\right)-1$ fits the expression in the radical But not sure how to set up the substitution -
MHB -z.61.W8.6 int sin^2(x)cos^2(x) dx
Evaluate $\displaystyle \int\sin^2 \left({x}\right)\cos^2 \left({x}\right)$ $\displaystyle \sin^2\left({x}\right) =\frac{1-\cos\left({2x}\right)}{2}$ and $\displaystyle \cos^2 \left({x}\right) =\frac{1+\cos\left({2x}\right)}{2}$ So $\displaystyle \int\frac{1-\cos\left({2x}\right)}{2}... -
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Show that ∫ dx |f(x)|^2 = ∑ |Cn|^2
Homework Statement This is a question regarding Fourier series. ∫ dx |f(x)|^2 = ∑ |Cn|2 (note the integral is between -π and π, and the sum is from n= -∞ to ∞)Homework Equations Complex Fourier series: f(x) = ∑Cn einx (again between n = -∞ and ∞) The Attempt at a Solution So I figured the...- Poirot
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- Dx
- Replies: 12
- Forum: Calculus and Beyond Homework Help
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I How Do You Solve the Integral of 1/(y+cos(x))^2?
First part of the question was to work out the integral 1/(y+cos(x)) between x=0 and x=pi/2 by using the substitution t=tan(x/2). Got this to be \frac{2}{\sqrt{y^2-1}}arctan(\sqrt{\frac{y-1}{y+1}}) The next question says HENCE find integral with the same limits of \frac{1}{(y+cos(x))^2} Ive...- Needhelp62
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- Replies: 7
- Forum: Calculus
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Calculating Integral: ##\int_a^b x\left(\frac{b-x}{b-a}\right)^{n-1} \; dx##
Homework Statement How do I calculate ##\int_a^b x\left(\frac{b-x}{b-a}\right)^{n-1} \; dx##? Homework EquationsThe Attempt at a Solution I tried the substitution ##u = \frac{b-x}{b-a}## to no avail. Someone please help.- squenshl
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- Forum: Calculus and Beyond Homework Help
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MHB How to Integrate cos^2(x)sin^3(x) dx?
$$\int \cos^2 \left({x}\right)\sin^3 \left({x}\right)dx$$ $$-\int\cos^2 \left({x}\right)\left(1-\cos^2 \left({x}\right)\right)\sin\left({x}\right)dx =-\int\left(\cos^2 \left({x}\right)-\cos^4\left({x}\right)\right)\sin\left({x}\right)dx $$ $$u=\cos\left({x}\right)\ \ du=-\sin\left({x}\right)dx... -
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How Do You Integrate tan²x sec^4x dx?
Homework Statement the correct solution is ∫ tan²x sec²x sec²x dx = replace the first sec²x with (tan²x + 1): ∫ tan²x (tan²x + 1) sec²x dx = expand it into: ∫ (tan^4x + tan²x) sec²x dx = let tanx = u differentiate both sides: d(tanx) = du → sec²x dx = du substituting, you...- hotjohn
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- Forum: Calculus and Beyond Homework Help
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How to Integrate tan 2x?
What is ##\int \tan 2x \ dx##? What I get is ##\int \tan 2x \ dx## ##= \int \frac{\sin 2x}{\cos 2x} dx## ##= \int \frac{2 \sin x \cos x}{1 - 2 \sin^2 x}dx## let u = sin x then ##\frac{du}{dx} = \cos x## or du = cos x dx So ##= \int \frac{2 \sin x \cos x}{1 - 2 \sin^2 x}dx## ##= \int... -
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Understanding dx in Integration
Hello, I am currently in my first year of college, and I already took calculus in high school. I was able to solve all the problems, but I feel like I didn't understand everything conceptually. When integrating dy/dx=x you get, ∫x dx=1/2x2. But what exactly happened to the dx, why did it... -
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Thermodynamics: Relationship between deltaX, partialX, dx
Homework Statement I am trying to understand the the following derivation: Cv = (qv/ΔT) = (ΔU/ΔT) \\ Cv = (∂U/∂T)v \\ dU = CvdT The Attempt at a Solution [/B] So here is what I understand so far. I understand that heat transfer q and temperature T are related by a direct...- ybhathena
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- Replies: 8
- Forum: Introductory Physics Homework Help
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Can you derive a trigonometric function from its inverse dx?
Homework Statement Arbitrary derivative of inverse trigonometric function: (sin-1x) = 1/(√1 - x2) Homework Equations f-1(f(x)) = 1/f`(x) The Attempt at a Solution So basically I learned about derivatives of trigonometric functions in class, and I thought maybe this would work: deriving the...- Eclair_de_XII
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- Derive Dx Function Inverse Trigonometric
- Replies: 9
- Forum: Calculus and Beyond Homework Help
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Why can "dx" in integration be multiplied?
Hi, This is an example in "Barron AP calculus" I learned from some past threads that "dx" in integration either means △x which is a infinite number or indicates the variable with respect to which you're integrating. In the equation above, it seems that dx is multiplied by (1-3x)^2. Isn't dx...- Kelly333
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- Dx Integration
- Replies: 9
- Forum: Calculus
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Integrating dx / (4+x^2)^2 using Trigonometric Substitution
Homework Statement Evaluate the integral: integral of dx / (4+x^2)^2 Homework Equations x = a tan x theta a^2 + x^2 = a^2 sec^2 theta The Attempt at a Solution x = 2 tan theta dx = 2sec^2 theta tan theta = x/2 integral of dx / (4+x^2)^2 = 1/8 integral (sec^2 theta / sec^4 theta) d theta =...- Oribe Yasuna
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- Forum: Calculus and Beyond Homework Help
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MHB -z.57 dx formula that estimates the change
Write a differential formula that estimates the change in the volume $V=\frac{4}{3}\pi{r}^{3}$ of a sphere when the radius changes from $r_0$ to $r_0+dr$ $$dV=4\pi{r}_{0}^{2}dr$$ this was one of the selections but I didn't know how to account for the $r_0$ to $r_0+dr$ -
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Difficulty understanding ∫ P(X).X^2 dx = <X^2> ?
I know for discrete random variables Σ P(x).x = <x> Translating for continuous random variables I'm also aware of the result ∫ P(x).x dx In my lecture notes ( I more or less transcribed from what the lecturer said ): ∫ P(x).x^2 dx = <x^2> , should it not be ∫ P(x^2).x^2 dx = <x^2>? Does...- Yungphys
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- Difficulty Dx
- Replies: 2
- Forum: Set Theory, Logic, Probability, Statistics
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Definition of dx: What is its Domain & Formalization?
Homework Statement http://imgur.com/goozE9f Homework Equations ##(dx_i)_p i= 1,2,3## 3. The Attempt at a Solution [/B] I'm reading Manfredo and Do Carmo's Differential Forms and Applications. This is the very first page Would you mind explaining me what is meant by dx, as highlighted in the...- brunoschiavo
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- Forum: Calculus and Beyond Homework Help
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How Do You Integrate (dx/dt) dx in Physics Problems?
Good Night, Can someone please tell me how to do: ∫ b (dx/dt) ⋅ dx ? Like in the work done by a force which is proportional to the velocity (like drag). I tried to change dx to v dt but couldn´t go much further. Thank you in advance.- danunicamp
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- Forum: Calculus
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MHB Stumped by Definite Integral: $\int_1^2 \frac{\sin(x)}{\sqrt{x^2-1}} \, dx$
Was asked to solve this definite integral in a tech free test. Not sure how to go about it. $$\int_1^2 \frac{\sin(x)}{\sqrt{x^2-1}} \, dx.$$ I know here is a relationship between inverse sin and the sqrt function but with just sin x?- Bushy
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- Definite integral Dx Integral
- Replies: 1
- Forum: Calculus
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Relativity: Exploring dX and dY in Math
Dear PF Forum, I'm studying Relativity, And there's some term in math that I don't know. And I am even not an English native. in ##\frac{dX}{dY}## What does "d" mean? I know that dX is the tiny slice of X. What do we say it in English?- Stephanus
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- Dx Integral Relativity
- Replies: 41
- Forum: General Math
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Solving (x+1)^2 dx for Integration - Step by Step Guide
Hi, I literally just registered so I have no idea about forum rules, also I'm not good in english. 1. Homework Statement The equation is (x + 1)^2 dx. U = (x+1) DU = 1DX Homework EquationsThe Attempt at a Solution Here I get (U^3) over 3 times DX = (x^3 + 3x^2 + 3x + 1) over 3 times 1 I...- arianemati
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- Dx Integrating
- Replies: 4
- Forum: Calculus and Beyond Homework Help
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##\int\frac{2x+6}{(x-1)(x+1)^2} dx## ?
Hi I'm currently doing 'integral by substitution' part in a book. Although it is integral by substitution part, some exercises are solved using reduction of fraction and integral, without substitution. (Actually I can't solve some exercises if I use substitution and the book's explanation also...- Byeonggon Lee
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- Replies: 9
- Forum: Calculus and Beyond Homework Help
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Integrating dx and dy: What Does It Mean?
Once you've integrated, dx and dy just indicate what variable you've integrated in terms of, correct?- Blue and green
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- Forum: Calculus
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Differential of X [ dX = U/V dV + U/p dp ] Internal Energy?
Homework Statement dX = U/V dV + U/p dp Write the differential of X in terms of the independent variables.Prove that this is an exact differential.Use the ideal gas equation of state to verify that X is actually the internal energy and that it satisfies the above equation. Would...- says
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- Replies: 7
- Forum: Introductory Physics Homework Help
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Why Does My Integral Calculation Differ from the Expected Result?
The result of the integral of (1/2)sin2x dx with: upper limit x = arccos((R-h)/R) lower limit x = 0 is (-h^2+2Rh)/(2R^2) I can not seem to get this exact answer my workings yield: let u = 2x, du/dx = 2 therefore dx = du/2 Integral becomes (1/4) ∫ sinu du (with the same upper and lower...- J_M_R
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- Dx Integral Trigonometery
- Replies: 2
- Forum: Calculus
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What is the integral of e^-(x/2) * sin(a*x) dx?
what is the integral of e^-(x/2) * sin(a*x) dx??- Emmanuel_Euler
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- Forum: Calculus
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Indefinite and definite integral of e^sin(x) dx
Look to this indefinite integral →∫e^(sin(x))dx Antiderivative or integral could not be found.and impossible to solve. Look to this definite integral ∫e^(sin(x))dx (Upper bound is π and Lower bound is zero)=?? my question is : can we find any solution for this integral (definite integral) ??- Emmanuel_Euler
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- Forum: Calculus
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What is the interpretation of dx in calculus?
Apologies if this isn't quite the right forum to post this in, but I was unsure between this and the calculus forum. Something that has always bothered me since first learning calculus is how to interpret dx, essentially, what does it "mean"? I understand that it doesn't make sense to consider...- "Don't panic!"
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- Replies: 48
- Forum: Differential Geometry
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MHB Integrating $\int x^2\cos\left({\frac{x}{2}}\right)dx$ by parts
$\int x^2\cos\left({\frac{x}{2}}\right)dx$ $u={x}^{2}\ dv=\cos{\left(\frac{x}{2}\right)}dx$ $du=2x dx\ v=\int\cos\left({\frac{x}{2}}\right)dx=2\sin\left({\frac{x}{2}}\right)$ Integrat by parts, just seeing if getting started ok -
Integrate x^2 / (x^2 + a^2)^3/2 dx
Homework Statement My solution has two terms divided by a which is in error. I am a volunteer math coach to some junior college students and can't find my error in the problem. Its been a while since I earned my masters in electrical engineering. The issue is the presencce of the variable...- Ray Beaver
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- Replies: 5
- Forum: Calculus and Beyond Homework Help
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How to Determine Frame Size with Lorentz Transformation
First time posting in this section. I understand that this question could possibly be an old and common question about Lorentz Transformation, however I failed to find useful discussions or instructions online. Assuming that there're 2 frames ##S, S'## where ##S'## moves along the ##x_{+}##...- genxium
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- Replies: 4
- Forum: Special and General Relativity
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MHB How Can I Use Substitution to Solve This Integral?
$$\int\frac{2x}{x^2+9}\ \text{dx}$$ I thot I could use $$u={x}^{2}+9$$ But counldn't go thru with it -
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Integral and dx inside function
Im working on a problem whit the follewing integral: I = \int|f(x+dx)dx| Im trying to use int by parts : t = x + dx \Rightarrow dt/dx = 1 + ddx/dx = ?, but i have no idee on what ddx/dx is? I think dx -> konstant? so ddx/dx = 1 ? -
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Compute ∫√(25 - x^2) dx from 0 to 5 using an infinite Riemann Sum
Homework Statement Integrate √(25 - x^2) dx from 0 to 5 using an infinite Riemann Sum Homework Equations lim n→∞ Σ_(i=1)^n i = n(n+1)/2 lim n→∞ Σ_(i=1)^n i^2 = n(n+1)(2n+1)/6 The Attempt at a Solution Δx = (b - a)/n Δx = (5 - 0)/n Δx = 5/n f(x_i) = √(25 - [a + iΔx]^2) f(x_i) = √(25 - [0 +...- s3a
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- Dx Infinite Riemann Riemann sum Sum
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- Forum: Calculus and Beyond Homework Help
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MHB How Do You Integrate $\int \frac{1}{1-e^x} dx$ with Substitution?
$\int \frac{1}{1-e^x} dx$ $u=1-e^x,\ du=-e^x dx$ Not sure of next step -
MHB What is the Integral of e^√x/√x?
$$\int\frac{e^{\sqrt{x}}}{\sqrt{x}}dx$$ ok I set $u=\sqrt{x}$ and $du=\frac{1}{2\sqrt{x}}dx$ I thot I would find a table reference for this but not sure which one could be used so now we have $$\frac{1}{2}\int\frac{e^{u}}{u}du$$ but maybe better way -
Integrating cos^2x with the Chain Rule: Explanation and Example
Homework Statement ∫cos2x dx The Attempt at a Solution I know the answer, and i know how to get there using: cos2x+sin2x=1 cos2x-sin2x=cos2x cos2x=(1+cos2x)/2 But why can't i use the chain rule? Can i?- johann1301
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- Forum: Calculus and Beyond Homework Help
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Integral x^n *f(x) dx =0 ; f for all n, f in C[0,1], then f(x)=0
I am trying to show that for f in C[0,1] , and ##n=0,1,2,... ## we have: ## \int_0^1 x^n f(x)dx =0 ## (&&) , then ##f(x)==0 ## . I am using Weirstrass approximation, so that , for any ## \epsilon >0 ## , there is ## P_n(x) = a_0+a_1x +..+x^n ## with : ##Sup_{x in [0,1]} |...- WWGD
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- Replies: 4
- Forum: Topology and Analysis
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Trapezium rule, what does dx represent
Homework Statement What does the "dx", associated with the definite integral represent for the trapezium rule? Could dx=h? (the heights of the trapeziums) Homework Equations The Attempt at a Solution- Rochefort
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- Dx
- Replies: 11
- Forum: Calculus and Beyond Homework Help
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Integrating tan^3 x: Tips and Tricks for Solving ∫tan3x dx
Homework Statement ∫tan3x dx 2. The attempt at a solution ∫tan x + ∫tan2x ∫tan x (sec2x - 1) dx ∫(tan x (sec2x - tan x) dx ∫tan x sec2x dx - ∫tan x dx u = sec x du = sec x tan x dx ∫tan x sec x sec x - ∫tan x dx Now I'm stuck.. ∫ du * u - ∫ tan x dx ?- Cali920
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- Forum: Calculus and Beyond Homework Help
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Finding Integrals: ∫ (5x^2 + sqrt(x) - 4/x^2) dx
I have these integrals to find: ∫ (5x^2 + sqrt(x) - 4/x^2) dx ∫ [cos(x/2) - sin(3x/2)] dx ∫ s/sqrt(s^2 + 4) ds (upper coordinate is 5 lower coordinate is 1) I have worked it out as: ∫〖(5x^2+√x〗-4/x^2) dx=5x^3/(2+1)+x^(1/2+1)/(1+1/2)-4x^(-2+1)/(-2+1)+C=5/3 x^3+2/3x^(3/2)+4/x+C...- Mathsishard123
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- Replies: 7
- Forum: Calculus and Beyond Homework Help
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Why do we write dx in indefinite integrals
in understand why we write the dx in riemann integral , but in the indefinite integral why do we use that ? what is the relation between the area under a curve , and the antiderivative of that of that curve ??- KingCrimson
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- Dx Indefinite Integrals
- Replies: 12
- Forum: Calculus