What is Integrate: Definition and 650 Discussions

Homework Statement \int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x The Attempt at a Solution If I use u = \pi-x I get : \int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x = \int_{0}^{\pi} \sin ( \cos x ) \mbox{d}x but then what?

How do you integrate (ln ln x)^n for any n?

~~ Integrate 3cos^2(x) Hey guys, Can you please show me a step by step integration for Find the solution for the differential equation : 3Cos2(x) , y= Pi , x = Pi/2 Thank you !

How does one integrate \int_0^\infty e^{-\beta x^2}\cos{(bx)} dx for positive beta and real b ? I was thinking maybe differentiation under the integral sign would do the trick, but I can't get anywhere.

how do i integrate this?? how do i integrate this function? \intdx/(ex-1)0.5 i have tried all the methods i know and haven't cracked it, the best try i have had so far is \intdx/(ex-1)0.5 ===>t=ex; dt=exdx \intdt/t*(\sqrt{t-1}) now from here i tried integration in parts and...

\int e^\sqrt[3]{x} dx Integration by parts, perhaps? But if that's the case, I have no idea which is right value for u and which is the right one for dv... Taking ln on both sides? Uh...hmm...I don't think that's how you work this question out... Any ideas, guys? :| Thanks!

how do i integrate this "e^[−(x/xa)]

Say you have an arbitrary function f(x,y) and you have the partial derivative fx How would you go about finding the general form of this integral? \int f^{5}(f_{x}+2f_{y}) I wanted to treat fx+fy = df, but the constant 2 really messes that up.

i now need to integrate the time-dependent schrodinger equation in 2D the potential is rotationally invariant and so is the initial wave function thus the symmetry of the initial wave function will be preserved in time Instead of a 2D equation, i now only need to integrate a 1d equation...

Homework Statement 18\int_0^4 \sqrt{4- (y-2)^2}dy Homework Equations According to the textbook l am supposed to use y=2sin\theta for substitution The Attempt at a Solution y=2sin\theta dy=2cos\theta d\theta 18\int_0^4 \sqrt{4-...

Homework Statement This is extra credit, and the test has passed (no one got it), the prof said he'll still take efforts on it so here is my attempt. A rocket sled is going down a test track at 180 km/hr (calculated to 50 m/s). It drops a snorkel into a trough of water. This diverts 30...

This is extra credit, and the test has passed (no one got it), the prof said he'll still take efforts on it so here is my attempt. A rocket sled is going down a test track at 180 km/hr (calculated to 50 m/s). It drops a snorkel into a trough of water. This diverts 30 kg/s of water vertically...

Homework Statement I've got B as a function of r B[r] B'[r] for derivative B[r] with respect to r and C for constant Homework Equations \mathbf{\frac{\ B'[r]}{\ r B[r]^2}}+\mathbf{\frac{\ (B[r]-1)}{\ r^2 B[r]}}= C solve for B as a function of rThe Attempt at a Solution I try to separate...

Problem: \int\sqrt{x^{2}+2}/x Attempt: Let x= \sqrt{2} sin\vartheta dx= \sqrt{2} cos\vartheta d\vartheta from this I got \int\sqrt{2}sin\theta\sqrt{2}cos\theta/\sqrt{2}cos\theta I think inverse substitution was not the right way to solve this problem... any help would be greatly...

Homework Statement Define I(x)= I( x - x_n ) = { 0 , when x < x_n { 1, when x >= x_n. Let f be the monotone function on [0,1] defined by f(x) = \sum_{n=1}^{\infty} \frac{1}{2^n} I ( x - x_n) where x_n = \frac {n}{n+1} , n \in \mathbb{N} . Find \int_0^1 f(x) dx ...

Homework Statement Integrate sinx*sqrt(1+((cosx)^2))dx Homework Equations integral udv = uv - integral vdu The Attempt at a Solution I tried integration by parts which is: integral udv = uv - integral vdu I tried substituting (cosx)^2= 1-(sonx)^2 neither of them seemed to work...

Hello, I have a really complex function to integrate (not homework), and I was wondering if there is any software application that can handle it. I have tried MathCAD and Maple, but both can't perform it. I don't think I can do it by hand, with all the integration by parts and expansions...

Hi, I am trying to work a problem that seems to have me stumped. ∫x/√(x+1) dx I have tried to look at it as a right triangle with: hypotenouse = √(x+1) sideA = 1 sideB = √x So I have: cot^2 ∅=x, dx=-2cot∅csc^2 ∅ d∅ csc∅=√(x+1) Working through the problem I have -2∫(cot^2...

Homework Statement For whatever reason, I'm having issues integrating sin2(x) Homework Equations I can use U-sub, trig-sub, integration by parts, partial fractions, in any combination as needed The Attempt at a Solution My brain is failing me, so any hints would be awesome.

it seems you can't use the property ln x^n = n ln x. I'm thinking there's integration by parts involved but not sure.

Here's the question: integrate the function cos(sqrt(5t)) with lower bound: x and Upper bound: 6

what is the best way to integrate this functio, i integrated in parts f(x)=x2/2x+3 i split the top of the fraction and then integrated the x2 half using integration in parts, but its just long and lots of place to make mistakes.

I've been reading up in the help files on MATLAB for this one, but it's a bit tricky. I have been able to solve it on my own by using a FOR loop, but it's not completely accurate as it's just adding up rectangles at the average between two values. Here's the problem: Does there exist a...

Hey all! It's been a while since I've done this, how do you integrate a rational function, where the denominator cannot be factored, again? For example, \int \frac{x}{x^{4}-1} dx Thanks, in advance!

Homework Statement how do i integrate sec^2(x) i completely forgot how to do this one. i know i could rewrite it as: tan^2(x) + 1 and integrate that, but i forgot how to integrate that 1 too Homework Equations The Attempt at a Solution

This is not homework, but I'm just wondering, how do you integrate this deceptive looking integrand to get what Wolfram has? I don't get why the answer has an inverse hyperbolic function. Please teach me!

\intx*arctg(1/x)dx i have such problems integrating arc functions, don't know why, but they never turn out right,, by using \intudv=uv-\intvdu u=x du=dx dv=arctg(1/x) v=[1/(1+(1/x)2)]*ln|x| =[x2/1+x2]ln|x| \intx*arctg(1/x)dx=x*arctg(1/x)-\int(x3ln|x|)/(x2+1)dx now...

\int e^xlog(x) I have solved this sum using integration by parts. The answer which i get is e^xlogx - logx - \sum^{\infty}_{i=1}\frac{x^i}{(i)(i!)} But i also used the series expansion of e^x. Is there any other way of doing this sum? I have almost tried out every single way of doing this...

Anyone know how to integrate this? Thanks

Hi, This is probably a really simple question, but I think that I am getting lost in notation. I want to integrate the following over all values of the (2-dimensional) vector \overline{r}: \int_{\overline{r}} \frac{\delta(\abs{\overline{r}-L})}{2\pi L} \overline{r} d\overline{r} Basically...

First of all, hi I'm new here my name is crisanna. I stumbled upon this site across the web and realized this 's a great site! Anyway , here 's my question. Does anyone know how to integrate sin (1 +cos ^2 x) ? I tried the method integrate by parts but I got stucked. Below is my attempt : u=...

Hi all. can anyone integrate xdx/x^2+4x+5 and this one : xdx/sqrt(x^2+4x+13) thank you and excuse me for english:)

(Tanx)^2(Secx)

Could someone show me how to integrate this. Bear in mind 'a' could be positive or negative thus i don't think we can use sqrt(a) in our answer...

I believe the answer is 0.5(x(x^2-a)^0.5)-0.5aln(x+(x^2-a)^0.5) does anyone know how to get this/derive this i.e. not take from tables ! Thanks

Hi, I am trying to find a solution for this equation in terms of r or t: \frac{d^2r}{dt^2} = \frac{m}{r(r-2m)}\left( \left( \frac{dr}{dt}\right)^2-\left(1-\frac{2m}{R}\right)\right) It seems I should integrate it twice with respect t, but I have no idea how to do that with a dr/dt term...

I have tried quite a few methods but haven't solved this problem, any help ? \oint axLn(x/b) dx where a and b are constants I have tried moving the 'a' outside the integration and solving xln(x/b) using integration by parts . I have also tried splitting xln(x/b) into xlnx -xlnb and...

I found this interesting little problem when thinking about convolution: \int x( \tau) \delta(t-\tau) d\tau Normally to solve something like this you would have to integrate by parts because of two functions in \tau Using the fact that: \int u *dv = u*v - \int v*du Where...

Hello, I am a researcher working on electromagnetic field. when solving the PDE equation, this integral about Bessel funtion arises: \int_{R1}^{R2} x J_1 (sx) dx where J_1 is the 1th order Bessel function of first kind, and s is a constant, R1 and R2 is integral interval. I have not...

Homework Statement n ∫2n-tdt 0 Homework Equations N/A The Attempt at a Solution I've been wondering about the correct way to deal with this type of integral for quite a long time. To me, the above integral looks like something of the form: n ∫f(n,t)dt 0 n appears in the...

I'm stuck on a calculus problem. The intagral (from 0 to 2) of (x-4)/(x^2+4) I figure you can split it as x/(x^2+4) - 4/(x^2+4) but I have no idea what to do after.

I have a cylinder of height 2a and radius R centered at the origin, and I want to integrate 1/r over it. Ie: I=\int_{V}\frac{1}{\left|\texbf{x}\right|}d^{3}\texbf{x} I know how to do it: I=\int^{}_{}\int^{}_{}\int^{}_{}\frac{\rho d\phi d\rho dz}{\sqrt{\rho^2+z^2}} But I'm wondering...

The question is to convert the infinity limits of the integral \int^\infty_{-\infty} e^{{-x}^2} dx to finite limits \int^{u_a}_{u_b} g(u) du using the substitution u = tanh(x). How do I go about it?

hi there.. I want to know how to integrate inverse trigonometric functions?like inverse tanx for example? thanx a lot..I just want a brief explanation?

Well, so I really want to integrate what's shown in the title: i.e. \int \frac{dx}{(x^2+y^2)^\frac{3}{2}} Now, I know there are quite a few straightforward answers to this. But what I really want is how people who do math got this formula in the first place. I don't just want a formula that...

which will yield the simplest partial derivatives i.e. integrate over the xy plane if dz/dx and dz/dy yield the simplest expression?

Please help me integrate homework :( [/tex]Homework Statement Homework Equations \int dx/(1-x^2)^3 The Attempt at a Solution I believe I have to use partial fractions to solve this integral. I started out by expanding the denominator 1/-(1 - 3x^2 + 3x^4 - x^6) I pulled out...

Homework Statement i do not know where to start with this one can anyone point me where to go please? \int \frac{1}{x^{4}+1} lower limit = 0 upper = infinity Homework Equations like i said i don't know where to go with this one. i mean i know I am going to have to do...

Hi! I have to integrate on a triangular domain \int_T f(x,y,z)dxdydz so I use simplex coordinates, i.e. x=(1-\alpha-\beta)x_1+\alpha x_2+\beta x_3 y=(1-\alpha-\beta)y_1+\alpha y_2+\beta y_3 z=(1-\alpha-\beta)z_1+\alpha z_2+\beta z_3 where (x_i,y_i,z_i) are the vertices of...

Firstly apologies for the calculation, where can I use equation editing software/fonts? Show that : dx = 1/6ln(7/4) where the limits are : b = 5 and a = 4 x^2 -9 I know that if the denominator was x^2 + 9 I could use 1/a tan-1 x/a + C . But...