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.

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  1. KingCrimson

    Solving Dy/Dx = 3-x/y+4: Integral of Both Sides

    there was this curve where Dy/Dx = 3-x/y+4 so he cross multiplied the equation as (3-x)Dx=(y+4)Dy , then he proceeded to integrate the function . i don't know if this is correct or not , i mean Dy/dx is just a notation , how can you treat as if it was just a normal fraction ? i thought...
  2. A

    What exactly is dx in an integral

    I'm doing integration by parts and I am a bit confused as to what exactly dx is. Usually when integrating it is just dropped or forgotten about. Now when doing integration by parts there are some problems where you pick x as your u and dx as your du. since du is the derivative of u why isn't the...
  3. J

    Dx as change in distance vs dx as infinitesimal x?

    dx as change in distance vs dx as infinitesimal x? Why are they the same notation?Sent from my iPhone using Physics Forums
  4. D

    How can I correctly solve the integral of e^x lnx dx?

    Homework Statement ∫e^x lnx dx I don't really know how to solve it. The Attempt at a Solution This is what i have: ∫e^x lnxdx = lnx e^x - ∫e^x/x dx And my prof says its wrong, that i can go further with it with some method they discussed about ( i missed it :(
  5. jdawg

    Solving an Integral Involving ∫(4x)/(x2+9) dx

    Homework Statement ∫(4x)/(x2+9) dx Homework Equations The Attempt at a Solution Originally I tried to solve with u substitution: u=x2+9 du=2x dx 1/2du=dx ∫2/u =2lnu+C =2ln(x2+9)+C But shouldn't arctan be somewhere in the answer?
  6. Crush1986

    How to solve the integral of Sech^5(x)*Csch(x) dx?

    Homework Statement integral of Sech^5(x)*Csch(x) dx Homework Equations I think Coth^2(x)-1 = Csch^2(x) may help The Attempt at a Solution I tried a few things. The latest being breaking the problem up and doing some re-working. int(Sech^2(x)*Sech^3(x)*Csch(x) dx) I then...
  7. I

    Solve Integral of y dx: Step-by-Step Guide

    Homework Statement Solve the differential equation: dy/dx = y+3 Homework Equations The Attempt at a Solution When I try to integrate with respect to x, I get ∫dy/dxdx - ∫ydx=∫3dx→y-∫ydx=3x So what does one do about the integral of y with respect to x? There is nothing...
  8. N

    How to find the function for which ∫ √x*√(1+y'^2) dx is stationary?

    this is an euler lagrange equation problem from the book- "classical mechanics-John R. Taylor", problem-6.11 find the path function for which ∫ √x*√(1+y'^2) dx is stationary. the answer is- x= C+(y-D)^2/4C, the equation of a parabola. here the euler lagrange equation will work on...
  9. J

    Power series for integral (1/x) dx

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  10. Y

    Integral of 1/(x^3 + bx - c) dx

    What is the integral of 1/(x^3 + bx - c) with respect to x? This is part of a larger problem I am working on, but finding the integral has proved a sticking point. I have simplified it as much as possible. P.S. The larger problem is finding J(r) in this PF post...
  11. C

    [HELP] How to integrate ∫ 1/(1-cosx)^2 dx ?

    [HELP] How to integrate ∫ 1/(1-cosx)^2 dx ?? Hi all, A very fundamental question here, but I cannot find solution from calculus books. Anyone know how to integrate ∫ 1/(1-cosx)^2 dx ?? Thanks.
  12. AakashPandita

    How do we integrate with respect to (dx)^2 (not dx)?

    ∫x(dx)^2=? and what is the difference between dx^2 and (dx)^2?
  13. S

    (Improper) Integral -2x/(1+x^2) dx from -INF to INF

    Homework Statement Consider the integral INT -2x/(1+x^2) dx FROM -INF TO INF (The attached TheIntegral.jpg file shows this in a more aesthetically-pleasing manner.) If the integral is divergent, state that it is so. Otherwise, evaluate the integral. Homework Equations Integration...
  14. H

    Finding dS in Polar: dx, dy, and More

    Ok, so we know that x=rcos(\theta) So what is dx? *** Furthermore, can I get dS in polar by finding dx and dy in polar and then substituting them into dS for rectangular? Is there an easier way to solve for dS in polar?
  15. S

    Integral of sin(x) sin(x+1) dx from 0 to 2pi.

    Homework Statement Integral of sin(x) sin(x+1) dx from 0 to 2pi. Homework Equations Integration by parts: Integral u dv = uv – Integral v du The Attempt at a Solution My work has been attached as MyWork.jpg. I, basically, get 0 * integral_I_started_with = something_else instead of...
  16. J

    Integral x^3sqrt(4x^2 -x^4) dx

    Homework Statement Integral x^3sqrt(4x^2 -x^4) dx Homework Equations Maybe something from a table The Attempt at a Solution I pulled the x^2 our from under the square root. ∫ x^4 (sqrt(4-x^2)) dx I'm not sure how I can do this one. Maybe it can fit the forum ∫ usinu du ?
  17. S

    Integral of 5x^2 /sqrt(4x-x^2) dx

    Homework Statement Integral of 5x^2 /sqrt(4x-x^2) dx. (This can also be seen in the attached TheProblem.png file.) Homework Equations Integration with variable substitution. The Attempt at a Solution Could someone please tell me what I did wrong in my work (which is attached as...
  18. S

    Integrating cos^6 (x) dx from 0 to pi/2

    Homework Statement This ( http://www.wolframalpha.com/input/?i=integrate+cos%5E6+(x)+dx+from+0+to+pi%2F2 ) is the integral I am trying to evaluate.: int cos^6 (x) dx from 0 to pi/2 Homework Equations (1 + cos(2x))/2 = cos^2 (x) (1 – cos(2x))/2 = sin^2 (x) sin^2 (x) + cos^2 (x) = 1...
  19. D

    MHB Simplifying the Integral of 20 sec^3(x) dx using Trigonometric Identities

    I'm having a hard time breaking this down using tri identities. } = integral sign 20}sec^3(x) dx 20}sec^2(x) * sec(x) dx 20}[tan^2(x)-1] * sec(x) dx after this I'm stuck. I tried letting u = tan(x) or sec(x) but i can't seem to cancel anything out.
  20. B

    MHB Show that ∫ logb(x) dx = x ∙ ( logb(x) - 1 / ln(b) ) + C

    Show that ∫ logb(x) dx = x ∙ ( logb(x) - 1 / ln(b) ) + C can you show me the complete solution to this prob? thanks!
  21. S

    Solving integral from 5/(x^2 + 1) dx from -1 to 1 works one way but

    Homework Statement The integral of 5/(x^2 + 1) dx from -1 to 1. (The TheIntegral.jpg attachment shows this in a aesthetically-pleasing way.) Homework Equations sin^2 (θ) + cos^2 (θ) = 1 1 + tan^2 (θ) = sec^2 (θ) cot^2 (θ) + 1 = csc^2 (θ) x = tan(θ) x = cot(θ) The Attempt at a...
  22. J

    Still confused about the dx notation

    So dx means an infinitesimally small change in x. Why is the slope written \frac{dy}{dx} instead of \frac{f(x)}{dx} since you are only making the x component infinitely small? When you take the integral you do ∫f(x)dx not ∫dy*dx
  23. W

    Compensation factor for converting dy dx to cylindrical coordinates?

    Homework Statement What is the compensation factor for converting dy dx to cylindrical coordinates? Homework Equations None that I know of besides the bottom ones as part of the attempt The Attempt at a Solution So I know that the conversion formulas for going from Cartesian (x,y,z)...
  24. V

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  25. M

    How Can I Integrate 1/(sin(x)+a) dx?

    Homework Statement Integrate ∫dx/(sin(x)+a), where a is a constant.Homework Equations The Attempt at a Solution I have been working on this for a while, and for some reason I can't figure it out. The attempt that seemed the most promising to me was to multiply top and bottom by (sin(x)-a)...
  26. Albert1

    MHB Evaluating the Integral $\int_{0}^{2\pi}x^2 cos(nx)\, dx$

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  27. I

    What's the difference between dx and ∂x?

    I understand from the equation: df = {\frac{\partial f}{\partial x}} dx + {\frac{\partial f}{\partial y}} dy that: dx \neq \partial x . I understand why df \neq \partial f (df is the change in f when the change in all the variables is infinitesimal, and \partial f is the change in...
  28. B

    Kinetic Energy: Exploring the Integral of Force and dx

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  29. J

    MHB Proving Lower Bound of $\int_{0}^{ \pi}\sin^{7}(x) \, dx$ is $(\pi/2)^7$

    Hi guys I have a doubt. How can I prove that (∫ (from 0 to pi) sin^7 xdx)(∫ (from 0 to pi) sin^(7/6) xdx)^6 is at most 128 But how can I prove that the lower bound of this expression is (pi/2)^7I think is a very interesting and not an easy question so any ideas? A guidance or something...
  30. V

    Integral of 1/sqrt(x)exp(-ix) dx using integration by parts

    Hi, Homework Statement I have already evaluated the integral 1/sqrt(x)exp(-ix) using The Residue Theorem and now I was looking for another method. So I thought of applying integration by parts and I got this attached formula. Now I am wondering how to evaluate this series. My first...
  31. Fernando Revilla

    MHB Int ( dx / x ^2 ) = - 1 / x, a new proof.

    Proposition. $\displaystyle \int\frac{dx}{x^2}=-\dfrac{1}{x} $ Proof. $$\begin{aligned}\int\frac{dx}{x^2}&=\int\dfrac{dx}{x\cdot x} \\&=\int\dfrac{d\;\not x}{x\cdot \not x}\\&=\left(\int d\right)\frac{1}{x}\\&=id\left(\frac{1}{x}\right) \\&=\frac{1}{x}\end{aligned}$$ Now, using the well-known...
  32. V

    Integral of 1/sqrt(x)exp(-ix) dx

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  33. V

    How can I solve the integral of 1/(1+x^4) from 0 to ∞?

    ∫1/(1+x^4) dx, from 0 to ∞ I have tried integration per partes, several different substitutions and transformation into different coordinate system but i have always only found another equivalent integral that i was not able to solve... I have also performed a numerical integration, but...
  34. r-soy

    MHB What is integration of y/(x^2-y^2) dx

    Hi all can please explaine to me what is integration of y/(x^2-y^2) dx step by step ...
  35. r-soy

    MHB What is integration of 1/(x^2-y^2) dx

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  36. G

    MHB What Does P(X ∈ dx) Mean in Probability Notation?

    Good day! I was trying to make sense of the notation $P(X \in dx),$ where $X$ is a continuous random variable. Some also write this one as $P(X \in [x, x+dx])$ to represent the probability that the random variable $X$ takes on values in the interval $[x, x+dx].$ I have seen similar notation a...
  37. Fernando Revilla

    MHB Ellen's question at Yahoo Answers ( Int 4 (tan ^3 x) dx )

    Here is the question: Here is a link to the question: How do you evaluate this integral: ∫ 4 (tan^3)x dx? - Yahoo! AnswersI have posted a link there to this topic so the OP can find my response.
  38. S

    Indefinite Integral of (3x^2-10)/(x^2-4x+4) dx using PARTIAL FRACTION

    Homework Statement Integrate (3x^2-10)/(x^2-4x+4) dx using partial fractions. Homework Equations None The Attempt at a Solution I tried using A/(x-2) + B/(x-2)^2 but I didnt get a coeffecient of an x^2. I've also tried using (Ax+B)/(x-2) + C/(x-2)^2 Though I...
  39. K

    Move 'dx' from 'dy/dx' to the other side, then integrate both sides

    I've been reading in my engineering textbooks and came across a frequent equation manipulation that involves multiplying/bringing the dx term of dy/dx to the other side of the equation, and then integrate both sides. I don't know what technique this is and I can't find it in my Stewart's...
  40. D

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    I have a question to ask, is dx = δx, can they cancel each other like \frac{dx}{δx}=1 and is it mean that: \frac{δf}{δx}\frac{dx}{dt}=\frac{df}{dt}? (f = f (x,y,z))
  41. M

    Exploring the Mathematical Conversion between ∆ and dX

    hi, Reading a book on thermodynamics and the guy often uses something like this : ∫1/T dQ = ΔS and then he says "this in differential form" : dQ/T = dS I kind of get the idea visually that one slice of "integral" will be dQ and you can think of it this way. But my question is how...
  42. R

    What is the Correct Approach for Solving ∫x^3*√(x^2-5) dx?

    Homework Statement ∫x^3*√(x^2-5) dx Homework Equations ∫u.dv=u.v-∫du.v The Attempt at a Solution So i tried to change the integral to ∫x*x^2*√(x^2-5)dx and u = x^2-5, then du = 2x, so 1/2*∫x^2*√(x^2-5) . Let u = √(x^2-5) , du = x/√(x^2-5) and dv = x^2 , v = x^3/3. Am I going in...
  43. B

    Integrate: (x^2 + 4)/ (x^2+5x-6) dx

    ∫Homework Statement "Express the integrand (what does "integrand" mean?) as a sum of partial fractions and evaluate the integrals. ∫(x + 4)/ (x^2+5x-6) dx Homework Equations The Attempt at a Solution x^2+5x-6 = (x-1)(x+6) Gives: ∫ A/(x-1) + B/(x+6) dx Findig A and B: A(x+6) + B(x-1)...
  44. B

    Mastering Integration by Parts: A Calculus 1 Student's Journey

    Hi all. I am having Calculus 1 this year. We are using a book called Thomas Calculus. I think its a lot of fun, but I have to work very much since there is basic stuff like trigonometry that I know really bad. Since I work so much with math I thought it could be fun and helpful to talk with...
  45. R

    Integrals of Exponential(Polynomial(x)) dx Form

    I'm curious about the general solution to \int_{-\infty}^{+\infty} \exp[P(x)] dx Where P(x) is a polynomial in x with real coefficients and whose leading (highest) order is even and its leading order coefficient is negative. Intuitively these integrals ought to converge, but I'm having...
  46. L

    Spring Compression problem- PLEASE SOMEONE HELP PLEASE DX<?

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  47. 5

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  48. J

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  49. N

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  50. A

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