What is Integrate: Definition and 650 Discussions

Homework Statement integrate dy/dx-y=cos(x)-2 Homework Equations The Attempt at a Solution dy/dx-y=cos(x)-2 is in the form dy/dx+p(x)=q(x) take the I.F as e^int(p(x))dx=e^-x multiplying throughout by e^-x d(e^-x)z/dx=-(cos(x)e^-x)-(2e^-x)...

Hi there people Can anyone help me with this issue? I'm trying to calculate this primitive P sqrt(x^2-4)/x^4 I tried the substitution x=2*sec(t) and it seems to work but at the end I get something like: 1/6*(sin(arccos(2/x)))^3 and this is quite different from what we can...

Homework Statement Okay this is part of a much bigger double integral, but I have hit a roadblock here. \intx1/u (top), 0 (bottom). (1-(x1/u))^a2 -1 ((x1/u) - x1)^a3 - 1 Homework Equations integration by parts/substitution? The Attempt at a Solution so first i set up an...

Homework Statement find general solution of dy/dx=xy+x using integrating factor Homework Equations The Attempt at a Solution rearange dy/dx-xy=x take integrating factor as e^int(-x)=e^-(x^2)/2 multiply throughout dy/dx(e^-(x^2)/2)y=(e^-(x^2)/2)x integrate...

Homework Statement Okay so today I started to learn about integration by parts and I understand the basics of it and can do some of the simpler problems, but this one made me stop. I have to integrate ln(x). I know the answer is xln(x) - x but I have to prove it.Homework Equations \int u dv =...

Homework Statement Calculate the antiderivative of the following: (202.31)/(1+e^(3.938-0.314x)) using either U-substitution or Parts but NOT partial functions. Homework Equations please show to me your work The Attempt at a Solution I'm not sure how to approach this, I'm stuck

Homework Statement A nonuniform thin rod of length L lies on the x axis. One end of the rod is at the origin, and the other end is at x = L. The rod's mass per unit length λ varies as λ = Cx, where C is a constant. (Thus, an element of the rod has mass dm = λdx.) Determine the gravitational...

Homework Statement trying to find the integral curve for ths equation get stuck at trying to integrate 10^-u dy/dx=10^x+yHomework Equations The Attempt at a Solution let u=x+y so dy/dx=10^u du/dx=1+dy/dx =(10^u)-1=du/dx du/dx=(10^u)-1 du/10^u=-dxthanks in advance

Homework Statement this is LFS of a question,which is (1+x)/(1-x-x^2) dx! i can not simplefy it at all b4 try to do d integration! Homework Equations The Attempt at a Solution

Homework Statement find total charge in a sphere with radius RHomework Equations integral with a circle in the middle( think its flux idk)) \int Eda=Q/eoThe Attempt at a Solution so i got and in the solution eo \int (kR^3 r^) (4 pie R^2)r^ for the answer they got eo(4pie kR^5) why didn't...

Homework Statement int [x2 / (x sin x + cos x)2]dx Homework Equations integration The Attempt at a Solution can anyone help me to start? thank you very much

Dear I am trying to integrate the following equation f=exp(m*x) dx where x =[x1 , x2] is a vector of variable could you help me please to find the solution when I would like to integrate like this kind of equations. help appreciated Best Regards

Homework Statement Find the integral of x over ((1+x)1/2-(1+x)1/3) dx Homework Equations integration by substitution. The Attempt at a Solution I have tried the substitution u = (1+x)5/6 but not really sure if this makes it any better! du/dx = 5/6 * (1+x)-1/6 6/5 * du =...

I am confuse a question state f(x) = (ln x )^2 ... i skip a part.. show that f'' (x) = 0 (not concern with the answer but what does f'' means is it that i have to differenciate twice or integrate twice..??) my second question: how to differenciate y = (ln x )^2

Homework Statement int((x^2)(e^-3lnx)) anyone tips for this?Homework Equations The Attempt at a Solution

Can't integrate the "e"s here Homework Statement \int 2/e3x(6+e-3x)dx Homework Equations I have no idea as to what equations to use, other than \int eu du = e u + C The Attempt at a Solution \int 2/(6e[SUP]3x[SUP] +1) dx u = 6e[SUP]3x[SUP] +1 du = 18e[SUP]3x[SUP] dx and...

How do you integrate Acos(\omegat + \theta) ? Where A is the amplitude, omega is angular velocity, and theta is position? I have no idea what to do. Should I U substitute?

Homework Statement Find the length of x=y^3/30+5/(2y) on 3 <= y <= 5 Homework Equations L = integral sqrt(1+(dx/dy)^2)dx The Attempt at a Solution I got to the integral upper bound = 5, lower bound = 3, sqrt(y^4/100+25/(4y^4)+1/2)dy. How do I actually solve the integral? It...

Trying to do an improper integral but for some reason am flummoxed by the integration of 1/sqrt(x-1).

How do I integrate sin(x^2) please? Not (sin(x))^2. Thanks again

I try to solve the integral 1/(1+x^3) dx , but I got stuck Now I got as solution: (1/3) ln(x+1) - (1/6) ln(x^2 -x+1) + (1/2) integral (1/(x^2 -x+1)) Can someone help me to solve the last integral? I have absolutely no idea how I can solve that one.. So integral: 1/(x^2 -x+1) dx

Use partial fractions to integrate x^3/(x^3+1)The Attempt at a Solution \int x^{3}/(x^{3}+1) dx Homework Statement Homework Equations The Attempt at a Solution \int x^{3}/x^{3}+1 dx I know that first i have to perform long division but i am at a loss how to do this THanks

Homework Statement Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region Homework Equations The Attempt at a Solution I got a...

Homework Statement Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. Homework Equations The Attempt at a Solution My result gave me an...

Homework Statement evaluate the iterated integral by converting to polar coordinates integral, integral x2dxdy, the limits are 4 to 0 for the outer integral, and /sqrt(4y-y2) to 0 for the inner integral. Homework Equations The Attempt at a Solution well...

Homework Statement x^2/(1-x) Homework Equations none The Attempt at a Solution I know I should use some kind of substitute but ... may t=1-x but what next ? any help will be helpfull thanks dimitry

Integral of dz/ (y^2 + (x-z)^2))^1/2

Describe the method you would use to integrate cot^a(x) csc^b(x) dx If a and b are odd? An explanation of the strategy would be a huge help!

how to integrate (1-x^2)^n for n \in N ? Limits of integral are from 0 to 1, but i don't think that matter. (i tried to use latex for int, but it wasn't working).

Homework Statement Integrate e^2x / SQRT [(e^2x) + 3)] Homework Equations The Attempt at a Solution i know the solution, is: SQRT [(e^2x) + 3] but i have no idea why. Please I need help thank you

How to integrate (x^3)(e^2x) ? Thanks.

My sister forwarded a link to me the other day about what I think can only be cause for disaster. The two most addictive things on the net are going to be working together to take over your life. That’s right, now you can post the status of your Kil’jaden raid party, or whoever is the...

Homework Statement Integrate cos[(pi/9)(x^2) Homework Equations Is there a trig identity for the cos(x^2) ? The Attempt at a Solution U=(pi/9)T^2 dU= [2(pi)/9] (T)dT dT= dU/ {[2(pi)/9 (T)]} Substitute in get cosU dU/ {[2(pi)/9 (T)]} Now what?

What method would I use to integrate cos(x)/1+sin^2(x)dx? I was thinking by parts but it isn't working for me.

I am absolutely stoned by this equation. I've looked through all the trig identities and the only one that comes close to be used in here is sin2u = 2sin(u)cos(u), but there is that lamba... Any suggestions?

Homework Statement S(x(x+1)1/2) dxHomework Equations The Attempt at a Solution u=x+1 du=1 x=u-1 S(x(u)1/2) du S(((u-1)(u)1/2) du S((u2-u)1/2) du S(u-u1/2) du S((1/2)u2-(2/3)u3/2) =(1/2)(x+1)2-(2/3)(x+1)3/2) + COnline homework says it's wrong... Where did I mess up?

how am i going to integrate this one? f(x) = sqrt( 1 + 1/x ) sorry for not using the symbol.. because not so familiar with that .. ^.^

If dy/dx = cosx sin2x and if y = 1 when x = pi/2, what is the value of y when x = 0? So, i separate the derivative into dy = cosx sin2x dx Then integrate both sides...this is where I'm stuck. How do you integrate cosx sin2x? I've tried u-sub and IBP but failed both times!

http://img717.imageshack.us/img717/4568/integral3.jpg I can see how to get to http://img179.imageshack.us/img179/3193/integral1.jpg but I'm not sure how the integral works I can integrate normal linear equations, trigonometric equations ect.. someone please show me qualitatively

How we can integrate this (without integration limits) sqrt (|x|)

Homework Statement \int x/(2x+1) dx Homework Equations The Attempt at a Solution I tried factoring out the 2 on the bottom to get 1/2 \int x/(x+1/2). then I put 1/2 \int x+(1/2)-(1/2)/(x+1/2) dx. from that i had, 1/2 \intdx - 1/2\intdx/(x+1/2) finally x/2 - 1/4 ln...

Gnuplot--how to find the area under a curve / integrate? I would assume this is a quite popular undertaking, so how is it normally done? I just want to know the approximate area under the curve if all the points were joined by straight lines, no need (or desire) for curve fitting. If I...

i have a second order ordinary differential equation of f(x): f''+(E-A(A+1)/x^2)f=0, where A is a positive integer, E is a real constant the domain is [0, \infty). the boundary condition is f(x=0)=0 since this is a linear equation, i only need to determine f up to a overall constant...

Homework Statement integral tan-1x dx i am supposed to integrate this by parts Homework Equations The Attempt at a Solution integral tan-1x dx = integral cosx/sinx dx u=cos x, du=-sin x dx v=ln sin x, dv= sin-1x dx integral cosx/sinx dx= cosx ln(sinx) - integral[ ln(sinx)(-sinx) dx] is...

Homework Statement Normalise Ψ(x,0) (use the fact that both ψ1 and ψ2 are stationary states). Will this wave function be normalised at any later time, t > 0? Homework Equations A particle in an infinite square well of width a has as its initial wave function an even mixture of the first...

Homework Statement Normalise Ψ(x,0) (use the fact that both ψ1 and ψ2 are stationary states). Will this wave function be normalised at any later time, t > 0? Homework Equations A particle in an infinite square well of width a has as its initial wave function an even mixture of the first two...

I've heard that there are some types of functions that are impossible to integrate. Can I see an example and why so? Thanks!

Hi again, I have a problem regarding improper integration. Homework Statement Refer to the image. I tried to solve and got zero for the answer. Is that correct? I refer to my actual problem it seem like it don't won't this way... Thanks

Homework Statement Integrate: (2x^2+1)e^x^2dx Homework Equations The Attempt at a Solution I don't even know where to start , I either got to do this by basic substitution or by parts. Basic substitution doesn't help for obvious reasons, so I thought I'd do it by parts, but that...

Homework Statement Integrate: (xe^x)/(sqrt[1+e^x]) Homework Equations The Attempt at a Solution I tried substituting u = e^x So the equation became: Integrate: ln|u|/sqrt[1+u] But... That doesn't help me. Trig substitution doesn't really help, neither does...