parts Definition and 817 Threads

Hi, J(m,n) = \int_0^{\frac{\pi}{2}} \cos^m \theta \sin^n \theta d\theta First of all I had to evaluate the following ( I don't know what the correct answers are but here are my calculations: J(0,0) = [\theta]_0^{\frac{{\pi}{2}}}=\frac{\pi}{2} J(0,1) = [-\cos...

Hello there. I feel like this isn't the right answer, but I'd like some verification as to where exactly I went wrong! 1. Homework Statement is \int_{0}^{pi}x^2cos x dx 3. The Attempt at a Solution went something like this: u=x^2 dv=cos x dx du=2x dx v=\int_{0}^{pi}cos x dx= sin x...

Homework Statement \int x^2*cosx dx Homework Equations The Attempt at a Solution Okay, so I started by making... u=x^2 du=2x dv=cos(x) v=-sin(x) Then I made the rudimentary equation: \int x^2 * cos(x) dx = -x^2*sin(x) + \int 2x * sin(x) dx Then I took the last integration problem (the one...

Homework Statement ∫ ln(x^2+14x+24) Homework Equations Integration by parts: ∫ udv = uv - ∫ vdu The Attempt at a Solution I chose u = ln(x^2+14x+24) and dv = dx therefore du = 2x+14/x^2+14x+24 and v = x Then once I substitute, I get: ∫...

Homework Statement indefinite integral dx/((e^x)(sqrt(1-e(-2x)))) using integration by parts evaluate the integral. Homework Equations integral u*dv = u*v- integral v*du The Attempt at a Solution To be completely and entirely honest i am not even sure where to start with this...

Homework Statement (1 / x * sqrt(4x^2 - 1))dxHomework Equations done by parts/trig?The Attempt at a Solution 1 = c 2x = b sqrt(4x^2 - 1) = a sin(theta) = 2x sin(theta) / 2 = x -(1/2)*cos(theta) d(theta) = dx cos(theta) = -2*sqrt(4x^2 - 1) I am not sure what to do about the x? Can I just...

First, hello all! Sorry if this is in the wrong forum (or wrong site, even), but I'm not sure where else to go, and I stumbled upon here doing some research (for project ideas). Feel free to delete this if it's off-topic. I am building a simple research project, and need some help choosing...

... of (x tan^2 x). i don't know how to do it. pls help

Homework Statement integrate arctan(1/x) Homework Equations The Attempt at a Solution z=arctan(1/x) dx=-dz(x^2-1) now its the integral of z(x^2-1)dz let u =X^2-1 du=2x dv=-udu v=-u^2/2 integral=(x^2-1)(-u^2/2) - int (-u^2)(2x) this is where i got stuck but i...

im having a bit of trouble, can anyone help me integrate arctan(1/x) using integration by parts? thanks

Homework Statement Use integration by parts to evaluate the integral: ∫ 1 ÷ (16 + x2) dx Homework Equations ∫ u dv = uv - ∫ v u' du The Attempt at a Solution That's the problem, I don't know how to start. How would I divide up 1/(16 + x2) into two? So there would be a value for u...

Hey y'all. I'm new to the forum, and have a problem that I've been working on all night long. I'm having issues previewing the Latex, so bear with me. I'll post the work I've done so far if the problem code shows up. Thanks. \int{\sin^{\frac{3}{2}}2\theta\cos^{3}2\theta} d\theta Now, the...

Homework Statement Hi, I've been having trouble solving the following problem, please help me. Question: (integration from 1 to 4) e^(x^(1/2))dx Homework Equations The Attempt at a Solution So far, i have done the following: u = e^(x^(1/2)) du =...

I am taking the liberty of collecting mathwonk's "short course" for some followup comments/questions, since this topic is IMHO more interesting than the context in which it first appeared. (Hope this is OK under PF rules!). Part I: Part II: Part III: How annoying, Part IV won't...

Hi, I have been working on this problem for the longest time and have just run in circles with it. I am thinking the answer is obvious but for some reason I am missing it. I need to find \int \frac{ln(x)}{x^2} dx I know that I need to use integration by parts and have tried a number of...

i know this is integration by parts so here is the problem I am currently confused on how the get an answer r e^r/2 dr I know I the formula is int udv= uv - int du v what i am not getting is what to use for this one. I figured e^r/2 = v and du = r so u= r^2/2 and what...

integral of (e^(2x))(cos3x)dx I get 1/2e^(2x)sin2x - 3/2integral(e^(2x)cos3xdx) what do i do next?

I did a few problems in integration by parts. There are two that I just can't seem to get. I've tried every type of subsitution or part I can think of. 1. e^sqrt(x) 2. sin (ln x)

"Evaluate the integral [0,1] x^3/sqrt[x^2 + 1] by integration by parts" I know I have to use the integration by parts equation, but I don't know what to make u and what to make dv..

Hello everyone. The book has this problem: (h) You are arranging six of your friends Alice, Bob, Charles, Diana, Francine, and George, in a row so that you can take their picture. (i). Alice and Bob have had a fight and refuse to stand next to each other. How many ways are there to...

integral y(1+y^2)^1/2 dy can someone help me with this? Thanks.

I have the expression \int{x(\ln{x})^3dx} I thought I had a quick way to integrate by parts but it turned out that I had accidentally evaluated \int{x\ln{x}dx} instead. Revisiting \int{x(\ln{x})^3dx}, I wanted to start by making a strange substitution, wherein u=ln(x), du=1/x dx, and x=e^u...

Problem: \int\frac{dx}{a^2-x^2} My Work: \frac{1}{a^2-x^2} =\frac{1}{(a+x)(a-x)}=\frac{A}{a+x}+\frac{B}{a-x}} 1=A(a-x)+B(a+x) If x=a, then 1=2Ba so B=\frac{1}{2a} Thus 1=A(a-x)+\frac{1}{2a}(a+x) if x=0, then 1=Aa+\frac{1}{2} so A=\frac{1}{2a} SO \int\frac{dx}{a^2-x^2}...

Hi all, I am having problems with the integral: \int e^{(ax)} cos(bx) dx I have got to \frac{e^{ax} sin(bx)}{b} - \int \frac{a e^{ax} sin(bx)}{b} dx After this I can only see myself going around in circles. Any help would be appreciated. :smile: Cheers, The Bob (2004 ©)

Hi, i am stumped on how to start this: integration of sin(ROOT(1 + x)) so, basically sin of square root 1 + x thanks James

kay I am having difficulties with this.. Knowing the gerneral formuala of |uv'=uv- |vu' i using a nonehomework question i was trying to make sure i had it down pat was having problems.. | x cos 5x dx but for some reason i don't get the right answer when it done... If I have u=x...

I need to find the integral of (x^2) 2 (secx)^2 tanx dx said aloud: x squared times by two times by sec squared x times by tan x I tried to use the [tex] function but failed misserably, hope you understand what i mean from what I've written above.

How do you evaluate \frac{1}{x\ln x} by integration by parts. I tried doing this doing the following: u = \frac{1}{\ln x}, du = \frac{-1}{x(\ln x)^{2}}, dv = \frac{1}{x}, v = \ln x . So I get: \int udv = uv-\int vdu = 1 + \int \frac{1}{x\ln x} = \int \frac{1}{x\ln x} . I know the answer...

I'm doing a problem where I'm supposed to use integration by parts. I have: Integral ln(x+3)dx u=ln(x+3) dv=dx du=1/(x+3) v=x integral ln(x+3) = xln(x+3) - integral x/(x+3) That's as far as I've gotten. I know that I should be able to find the integral of x/(x+3)...

So my problem is: a mass M that is fired at 45 degrees with KE E_0, at the top of the trajectory, projectile explodes with additional energy E_0 into two parts, the first fragment travels straight down , what is the velocity of the the first and the velocity and direction of the second part...

Could som1 please help me integrate arccos x by parts. I've done examples using integration by parts but they were all some form of multiplication, ie y = xe^x, y = x sin x etc. I'm really unsure where to start with this problem :confused:

I feel like I waste too much time on the wrong parts of lab reports... So I have a tendency to write a ton in my lab reports in the theory sections...we're talking 5-6 pages or more on theory. I enjoy doing this because it gives me the chance to kinda explain the concepts in my own words to...

Why is it that when I do integration by parts on cyclic functions such as (sinx)e^(inx), I get a trivial answer like C=C, C is a constant Have I done something wrong or are there other methods of doing those integrals?

in the diagram below Io is zero. But i can't figure out why. Can anyone explain this to me.

http://www.pbs.org/mediashift/2006/09/digging_deeperjournalist_paint.html" http://www.rsf.org/article.php3?id_article=18768" http://www.washingtonpost.com/wp-dyn/content/article/2006/08/26/AR2006082600297.html" I contend that for international affairs, there is an undeniable direct...

hello could someone give me a pointer here. this integral ∫ln(x + c)dx my guess is, by integration by parts (ab)' = a'b + ab' ∫ba = ab - ∫b'a so here a = ln(c + x) b = c + x a' = 1/(c + x) b' = 1 ab = (c + x)*ln(c + x) and ∫b'a = ∫ ((c + x)/(hc + x)) dx = ∫dx = x...

hi..im new to this topic..can someone check to see if this is right? \int (xe^-^x)dx = \int udV = uV - \int Vdu =x(-e^-^x)- \int -e^-^x =-xe^-^x-e^-^x+C thanks

Is it possible to produce electricity by using permanent magnets with no moving parts? I believe that is possible. Because AC current produced by moving armature or copper wire or some other metal in magnetic field. Then without moving wire it should produce DC or some kind of electron flow...

Hello I am teaching myself Quantum Mechanics from Griffiths. I have run into a mathematical problem which I need help with. As I have found no convincing answer, I am posting all the details here. Ref :Section 1.5 (Momentum) in "Introduction to Quantum Mechanics (2nd Edition)" by David J...

Hi, i am currently doing a project on these questions. 1)why do we feel heavier when the lift startes to move up? 2) why do we feel normal in the middle? 3) why do we feel lighter when the lifts comes to a stop? although i know that the three laws of Newton is somehow related to...

Can I use integration by parts recursively on this? \int (xe^x)(x+1)^{-2}

First off, I hope these images show up - I don't have time to figure out this latex stuff atm, so it's easier just to throw the formulae together in openoffice. I'm working on the Laplace Transform for http://home.directus.net/jrc748/f.gif Which is obviously...

Hi Can anyone pls suggest the trick to do integration by parts such as: Intergration {(1/x) (e^-cx) }dx. Which function normally we should take as first and second function. Is there a rule to decide on it. Plz reply thanks

So I'm trying to work-out the real and imaginary parts of a finite product, put P_n = \prod_{k=1}^{n} \left( x_k + iy_k\right) where the x's and y's are real numbers like you would expect.

I'm kind of lost on where to go next with this integration by parts problem. I have to integrate e^xcos(x)dx. I've gotten as far as one step of integration by parts, but I can't understand how this will help. It seems I'll just be going in circles. I have: e^xsin(x) - int(e^xsin(x))dx...

Okay, so here is the problem I have, which I am getting tripped up on for some reason: a) Use integration by parts to show that \int_{a}^{b} f(x) dx = bf(b) - af(a) - \int_{a}^{b} xf'(x) dx this was pretty easy, just regular old integration by parts with limits of integration. b) Use the...

Here's one for you: Can things be more than the sum of their parts? I'm going to share my answer later but for now I'm interested to here your thoughts. If you stop and think about it, it gets really tricky. Enjoy.

I am to find the imaginary part, real part, square, reciprocal, and absolut value of the complex function: y(x,t)=ie^{i(kx-\omega t)} y(x,t)=i\left( cos(kx- \omega t)+ i sin(kx- \omega t) \right) y(x,t)=icos(kx- \omega t)-sin(kx- \omega t) the imaginary part is cos(kx- \omega t) the...

Article below.

Integration by parts :( hi I have been trying this question for quite a while now and am unsure of what to do. Any help would be apprectiated. Integral x^13 cos(x^7) dx I know you have to use integration of parts. Here is what i have done so far: let U=x^3 dU =13x^12 dx dV=cos(x^7)...