Integrating Definition and 971 Threads

\int^{1}_{0}\int^{0}_{-x} \frac{ysin(pi*y^2)}{1+y} dydx Not exactly sue how to start this. I know that I need to integrate with respect to y first then use that solution and integrate again with respect to x however I do not believe integrating the initial problem is possible. Is there another...

Homework Statement So I thought of an interesting problem, and here it is: Solve \int \frac{1}{f'(x)} df(x) = g(x) for f(x). Now, I checked Wolfram-Alpha to see if an answer existed, and they gave me this: f(x) = c_1 e^{\int \frac{1}{g(\xi)} d\xi} But, you know that Wolfram-Alpha doesn't...

Homework Statement (2x+y^2) dx +4xy dy=0,y(1)=1 Homework Equations The Attempt at a Solution I'm having trouble finding the correct integrating factor, been playing with it for an hour and have made NO progress so need help. \delta P/\delta y=2y \delta Q/\delta x=4y...

I will denote vectors in bold. Homework Statement Show that the curve C given by r=a*Cos(t)Sin(t)i+a*Sin2(t)j+a*Cos(t)k ( 0=<t=<pi/2 ) lies on a sphere centred at the origin. Find \int zdS under C *edit* There is a huge gap here and the equation has dissapered for me. But...

Homework Statement Given \int_{0}^{k\pi} cos^{2m}(\theta) d\theta = A Express \int_{0}^{k\pi} cos^{2m}(\theta) cos(2\theta) in terms of A. Totally Stucked .. :XI've substituted cos^{2}\theta = \frac{1+cos(2\theta)}{2} Then i get 1/2 A + another chunck of integral. I've used...

Homework Statement Integrate sin5(x/3)dx on the interval [0,pi] Homework Equations sin2(x)=1-cos2(x) dcos(x)dx=-sin(x) The Attempt at a Solution I split off one of the sins and then set my integral equal to (sin2(x/3))2*sin(x/3) switching in 1-cos2(x/3) afterward. Then I set u =...

I was looking at how to derive an integrating factor for a non-exact DE that has multiple variable dependency, i.e. µ is xy-dependent, and I found the explanation at the link in the middle of the page at equation (22) (link...

Homework Statement Solve with u-substitution ∫ (x-5)/√(x-6) dx Homework Equations The Attempt at a Solution This is what I have done so far and it doesn't seem to work out. I have a feeling I'm missing something. Any help would be appreciated. u=x-6 du=dx x=u+6 ∫...

Consider I(c)= \int_0^\infty \frac{x^{1-\epsilon}}{x+c} dx For what values of \epsilon are these integrals convergent? Would it be \epsilon \geq 0? Then I'm asked to use x^{-\lambda} \Gamma(\lambda) = \int_0^\infty d \alpha \alpha^{\lambda-1}e^{-\alpha x} for x>0 and the identity...

Homework Statement The problem says to compute the following integral. \int_{C}F\cdot dr Where F=<e^y,xe^y,(z+1)e^z> \ \ and \ \ r=<t,t^2,t^3>,0\leq t \leq 1 2. The attempt at a solution Basically when I plug everything in, I get an integral that CANT be solved. At first I thought to...

Homework Statement Context is cosmology but not really relevant to the integration. I've managed to integrate it using substitution but it didn't seem that neat. Coming back after two-years off and I'm a bit rusty at spotting the best substitutions (wasn't great to start with :))...

Hi everyone I am looking at integrating this function, \frac{dv}{dt}=g-\frac{c}{m}v So far i have rearranged the function to get, (\int1/g - \int1/(cv/m))* dv= \intdt Thanks JB

Homework Statement Integrate dy/dx=2y+4x+10 The Attempt at a Solution dy/dx-2y=4x+10 Integrating factor = e^(-2)dx=e^-2x multiply both sides by IF. (e^-2x)dy/dx-2y(e^-2x)=(e^-2x)(4x+10) dy/dx(e^-2x y)=(e^-2x)(4x+10) i don't know what to do next.

I'm learning integration by parts, and thought this would be a good test of my understanding. I've separated it into something that seems better. \int \frac{1}{x^2+x}dx = \int \frac{1}{x} \frac{1}{x+1}dx I'm guessing I use integration by parts from here, but which should I make u?

Homework Statement Sorry asking similar quesion again about absolute value. You can read the attachment. u(x) is the integrating factor. Why absolute value is omitted in the integration? and why the integrating factor is not "1/|x|", with the absolute sign Homework Equations The...

Homework Statement Well hello! :smile: I am still uncomfortable with partials. In my (fluid mechanics) text we introduce this "stream function" \Psi(x,y) such that u =\partial{\Psi}/\partial{y} and v =-\partial{\Psi}/\partial{x} where u and v are the horizontal and vertical components of the...

Homework Statement trying to integrate this: \int^{\theta}_{\theta_{0}} \sqrt{\frac{1-cos(\theta)}{cos(\theta_{0}) - cos(\theta)}d\thetaHomework Equations My book tells me to let theta = pi - 2gamma and then simplify from there but I'm just not seeing that ! any hints? is there a trig...

Homework Statement The actual question is asking for the normalization constant for the wavefunction \psi\left(x\right)=A\sin^{5}\left(\dfrac{\pi x}{a}\right) without carrying out integration In short they want me to find the value of A such that A^{2}\int_{0}^{a}\sin^{10}\left(\dfrac{\pi...

Homework Statement Multiply the given equation by the given integrating factor and solve the exact equation. Homework Equations ydx+(2x-yey)dy=0, \mu(x,y)=y. The Attempt at a Solution M=y2, N=2xy-y2ey Integrating N=\Psiy WRT x I get xy2-((1/3)y3ey + y2ey)+h(x)=\Psi(x,y) Differentiating...

I am working on the following problem but I am apparently not applying the integrating factor correctly: The DE is: dy/dt = e^(-t/20) - (1/40)y I moved the last term to the left, giving dy/dt + (1/40)y = e^(-t/20). I had e^(t/40) as my integrating factor. Going in my (wrong) direction, I was...

The title contains the problem I have difficulty with. I understand I must use u substitution and then integrate by parts. So my actual problem is: How do I find the derivative of arcsin(x^2) if u = arcsin(x^2)? I know the derivative of arcsin(x^2) is 1/(1-x^2)^1/2 Thanks for...

Homework Statement [1/(x^4 - x)]dx Homework Equations The Attempt at a Solution I factored the denominator to x(x-1)(x^2 + x +1) and I'm not sure if I can use partial fractions.

Homework Statement use an integrating factor to solve \frac{ \partial u}{ \partial x} = -2 + \frac{u}{2x} The Attempt at a Solution let P(x) = \frac {1}{2x} M(x) = e^(\int(\frac {1}{2x}dx)) = \sqrt{x} so u = \frac{1}{ \sqrt{x}}...

Homework Statement I have work these two problems, but in the first one #4 I feel like I'm missing something a step or something. and in the second problem I'm just lost, I can't finish it so will you please assist me. your help is appreciated. Homework Equations thanks a lot. The...

Homework Statement Integral of dx/[(x2 - 2x + 2)2]Homework Equations Trig substitution rules: for expression sqrt(a2 - x2) make x = asin(t) with -(pi/2) < t < (pi/2) for sqrt(x2 - a2) make x = asec(t) with 0< t < (pi/2) and for sqrt(a2 + x2) make x = atan(t) with -(pi/2) < t < (pi/2)The...

Hello All, Given the equation (2/y + y/x)dx + (3y/x + 2)dy I am first asked to show the equation is not exact. To do this I showed the mixed partials were not equal i.e.: (2/y + y/x)dy != (3y/x + 2)dx I am then asked to find an integrating factor and show the potential function is given...

Homework Statement Ok, the problem is simple enough, I think. I just think I'm missing something obvious. I have an equation involving the scale factor R(t) and need to integrate it. I am at the first equation and need to get to the second by integrating (with respect of R, I suppose)...

how do i integrate 0.5e[SUP]t[SUP]

Hi, besides integration by parts, does anyone know of a simple integration trick to solve the integral (wrt x) of exp(x)*f'(x)?

Homework Statement Hey, I've been working through a book and one problem just gets me that I know should be a piece of cake. I don't know if I'm just being an idiot or not seeing something but the problem is to take int e^(ax)cos(bx)dx and int e^(ax)sin(bx)dx simultaneously by multiplying the...

0 \leq r \leq 1 -1 \leq z \leq 1 0 \leq \theta \leq 2\pi \int\int\int dV where dV = r dr d/theta r = 1 - z2 weird huh?

Homework Statement the problem is attached Homework Equations The Attempt at a Solution I don't understand to the Q but what i did is just integrating the dose rate , the Q is not clear to me can anyone help me

I'm really confused with how to prove this result...could anybody help please? Let I_{1} be the line segment that runs from iR (R>0) towards a small semi-circular indentation (to the right) at zero of radius epsilon (where epsilon >0) and I_{2} a line segment that runs from the indentation...

I'm not understanding why my answer is wrong Homework Statement \inttan^3(x) dx This is the solution I've been getting for this problem, but I notice you get a different answer when you let u = tan(x) and du = sec^2(x) dx Homework Equations tan^2(x) = (sec^2(x) - 1) The Attempt at a Solution...

Homework Statement INTEGRATE dx / (2 * root(x)) * (1 + x) Homework Equations That's pretty much it! The Attempt at a Solution I received this question on a Calc II exam, so I'm only looking for the solution for my own understanding (I'm sure I already got it wrong). My instinct...

Homework Statement xy' - 4y = x4ex Homework Equations The Attempt at a Solution y' - 4x-1y = x3ex x-4y' - 4x-5y = x-1ex I'm not sure what to do next, I can't express the LS as a derivative

Homework Statement Hi I have the following integral over wavevectors inside the Fermi circle (we are in 2D) \int {dk_x \int {dk_y \sin ^2 \left( {k_x x} \right)} } Ok, so I know that kx2+ky2=kf2, so ky2=kf2-kx2 - this takes care of ky. But what about kx? What should this run from in order...

Homework Statement Let P(v) represent the Maxwell-Boltzmann speed distribution. Basically what it comes down to is that I have to find the definite integral (0,inf) of P(v)*v^2 and get vrms from this. Homework Equations We are given the definite integral from 0 to inf for the function...

greetings what does a integrating factor tells about a differential equation? in order to find the solution for a exact equation we multiply the equation by integrating factor(I.F). as intergrating factor=e^integration(p)dx i.e given by I.F=e^gx where gx is integration of p now as we have...

Homework Statement [PLAIN]http://img580.imageshack.us/img580/9506/linegu.jpg The Attempt at a Solution Parametrising the curve C_1 as follows: {\bf p}(t) = (1-t)(1,4) + t(3,3) = (1+2t,4-t) {\bf p}'(t) = (2,-1) So \int_{C_1} = \bigg\{ \sqrt{\frac{y}{x}} \frac{dx}{dt} +...

By setting u = sin(x), I got 1/2 (sin(x))^2 By setting u = cos(x), I got -1/2 (cos(x))^2 The two answers are not the same, why are there two solutions?

Homework Statement Given that the probability of finding a 1s electron in a region between r and r + dr is: P = \frac{4}{a_{0}^{3}}r^{2}e-2r/a0dr work out the probability that an electron would be found within a sphere of radius: i) a0 Homework Equations The Attempt at a...

Homework Statement Hi Say I have the function f(x,y) = xy, and I want to integrate f(x,y) from (0,0) to some (px, py), where I know p^2 = p_x^2+p_y^2. What I have done is to write p_x ^2 + p_y ^2 = p^2 so the limits for px run from \pm \sqrt {p^2 - p_y ^2 }. Now, how about the limits...

For integrating over type 1 and type 2 regions, why does the g(x) or g(y) bound have to be the inner integral? Thanks!

Homework Statement Calculate the area under the curve for the following: f(x) = √x*√(−32 − x) and g(x) = √(−x2 − 32x) Homework Equations The Attempt at a Solution I've been trying to do partial integration since the functions f(x)=g(x)area are mirrored, so they are equal...

Find the volume of the finite region enclosed by the surfaces z = 0 and x2 + y2 + z = 1 I know I have to do triple integration on dV to accomplish this but do not know where to start and what limits to use for x, y and z? Cheers guys

I'm having some problems integrating fractions. If you could help me understand it, that would be great. Homework Statement \int\frac{2+3sin^{2}x}{5sin^{2}x}Homework Equations \int(x)dx=\frac{x^{n+1}}{n+1}The Attempt at a Solution...

Homework Statement \int\frac{x^{2}+2x+1}{x^{2}+1}Homework Equations INTEGRAL OF X=\frac{x^{n+1}}{n+1} I can't get the integral to work on the left side for some reason. The Attempt at a Solution I have completely forgotten how to integrate fractions. I know that "log(x^2+1)+C" would be...

Homework Statement The integral from v=vi to v of v^-2dv = -3 integral from t=0 to t of dt Homework Equations The Attempt at a Solution I am getting -1/v + C=-3t and the book is getting -1/v+1/vi=-3t. Not quite sure where they are getting 1/vi as I am getting C.

Hello I'm trying to solve the following DGL with an integrating factor: x'=xg(y) y'=yh(x) which is equivalent to -yh(x)dx+xg(x)dy=0 which is an inexact dg? How to i find an integrating factor in this case? thx