What is Integrate: Definition and 650 Discussions

Integrate the following: (x^3+x^2)/(1+x^4) I have been taught only integration by substitution. My teacher told me that this can be solved using that ith some trick. I have tried for a long time. All that I can do was to convert the numerator to x^2(x+1) and the denominator to...

Hey all, this should be a simple integral, but I can't seem to solve it. I tried some simple u-subs and integration by parts, but to no avail. Also, maple throws out some Fresnel function. \int_{-a}^{a} x^{2} cos\left( a x^{2} \right) dx

For those who want to understand why the integration of a function gives the area of it, you can take a look at... http://www.mathsroom.co.uk/downloads/Integration-Area_Under_A_Curve.ppt" I'm posting this because I think that not everyone who makes use of integration can really understand it...

i need help taking this integral \int 9sin\sqrt{t+1} help please! i don't even know where to start :[

Homework Statement Use the integration capabilities of a graphing utility to approximate the approximate the volume of the solid formed by revolving the region bounded by the graphs of y = sin x and y 0 in the interval [0, \pi] about the y-axis. Round your answer to three decimal places...

What is the best way?

Homework Statement Integrate f(x) = (x^3 + 3x + 12) / (x(x+2)^2) Homework Equations The Attempt at a Solution I know that i should somehow rewrite the polynomial but I do not know how. Please, help me.

Hello to everybody I'm trying to integrate this ODE but I don't know how: f'''+a*f*f''=0 where a is a parameter. With the boundary conditions f(0)=0; f(-inf)=1; f(inf)=1. I had thought about using a shooting method but I don't know how to apply it with these boundary conditions. It would...

Homework Statement Integrate e^(x^2) Homework Equations The Attempt at a Solution I have no idea at all..

Hello, I need to evaluate the following integral with respect to x. If you guys can give me some hints on how to start off, it would be greatly appreciated. f{x}(x) = \int\frac{\alpha\beta}{4}e^{(-\alpha|x| - \beta|y|)}dy The integral is evaluate from -infinity to infinity From this I know...

Homework Statement Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=7,and between the circles x^2 + y^2 = 196 and x^2 - 14x + y^2 = 0. Homework Equations The Attempt at a Solution i tried to double integrate...

Homework Statement int sqrt 8x-x^2 Homework Equations trig sub The Attempt at a Solution complete the square integral becomes int sqrt 16-(x-4)^2 let x-4= 16sin(Q) sqrt 16-(x-4)^2 =sqrt 16-256sin^2(Q) dx= 16cos(Q)dQ =...

[SOLVED] ff Homework Statement integrate (cos^2(x))/(sin^6(x)) Homework Equations Double angles? u-sub? The Attempt at a Solution I tried using double angles but I am really not sure what to do I havnt seen any like this... I have only done stuff without fraction like...

maple syntax: int(theta^y * exp(-theta*(1-alpha) ) , theta) I have a distribution that I need to integrate, and I know the result should have a gamma function in it. The only thing I have found helpful is: http://en.wikipedia.org/wiki/Gamma_function My function is kind of in that...

integrate this... integration of (tan inverse x)^2

Homework Statement Integrate from e^x to e^2x: (sin^2(t) + cos^2(t) -1)dt Homework Equations just standard integral equations The Attempt at a Solution I know how to do most of it, my only question is: is (sin^2(e^2x) + cos^2(e^x) -1) a special trig identity? or would i just...

[SOLVED] Integrate (1/(1-cos x)) dx Homework Statement \int \frac{1}{1-cos x} dx Homework Equations The Attempt at a Solution I found in the book where they used the cos x= \frac{1-z^2}{1+z^2}, but we haven't went over this in class yet. I'm wandering what my other options are...

How would I integrate e^(-pi^2*x^2) from -infinite to infinite? I know that the integral of e^(-x^2) from -infinite to infinite is sqr(pi), in which sqr is square root.

[SOLVED] why can't I remember how to integraTE x^2lnxdx ? I can't find a formula that matches up?

Homework Statement Volume enclosed by: z= x^2 + y^2 and z= 2y. This should look like 1/2 of a bowl only on the +y side of the x y z plane I believe. I want to know if integrating in different order or cord system will affect the result. I am having a lot of problems attempting...

Homework Statement integerate e^(8x^2) Homework Equations The Attempt at a Solution its seems it is not having closed integeral form.

I am working on an integral I am finding tricky, and I think I'm missing something. I need to integrate on the interval 0 to infinity, x²e^-x². We have proved that on the interval of -∞ to ∞, e^-x²=√∏ so from o to ∞, it equals √∏/2. I can use this in my proof, but I don't see how. When I try...

Homework Statement \intydx + zdy C where C is the part of the helix r(t)=(sin t)(i) + (cos t)(j) + t(k) and 0 < t < pi (those should be greater than or equal to signs) \int(cost)(cost)-t(sint) \int(1+cos 2t)/2 - t sint with limits from zero to pi. this then equaled to...

Homework Statement how do i integrate: (-2x)/(1+x^2)^2 Homework Equations The Attempt at a Solution I used the substitution u=1+x^2 then i got that the integral is 1/[2(1+x^2)^2 +C but I'm not sure if that's correct thank you

Homework Statement \int\frac{(5x+2)dx}{x-2} from 0 to 1 Homework Equations The Attempt at a Solution I've tried splitting it up into (5x)/(x-2) + (2)/x-2), but i couldn't go any farter. Ived also tried using lots of U subsitutions, but i can't figure out what do next. Is...

i am trying to integrate Integrate (5x+2)dx/(x-2) from 0 to 1. i have tried splitting the equation up into (5x)/(x-2) + (2)/(x-2) i have tried every U substitution i can think of but i can't figure out how to do it.

how do i integrate: square root of((x^2)-4) i know i have to use substitution but what do i substitute?

how do i integrate this?? a) ∫cot^(2)x cscx dx? b) ∫[x^(3) + 2x^(2) + x]^(1/2) dx

\int\frac{3x^4+4x^3+16x^2+20x+9}{x^5+2x^4+6x^3+12x^2+9x+18}dx I tried using du/u for Lnu but I couldn't get it into that form. I don't have any idea what to do next, really. Can someone point me in the right direction?

Homework Statement integrate 9/(3e^-6x + 3e^6x) The Attempt at a Solution integral :- the integral sign integral [ (9/3)(1/e^6x + e^6x)] 3*integral [ 1/((1+e^12x)/e^6x)] 3*integral [ (e^6x)/(1+e^12x)] Im stuck there. I thought I would get to something which I could...

Homework Statement Integrate... secx(tanx - secx) dx The Attempt at a Solution secxtanx - sec^2x dx = secx - tanx + C is that right?

Check out the link to see the problem and my work. Can anyone see where I made an error? I can't seem to figure out where I went wrong. https://www.physicsforums.com/attachment.php?attachmentid=11519&stc=1&d=1194912644"

integral calculus--pls integrate Homework Statement how do you integrate this one?what method do I have to use? \int\left\left[(u/\left(5u+11\right)\right]

Can you solve this \int \cos x^5 dx ?

In the course of working out a question, I came across a three dimensional integration in spherical polars. No while this shouldn't be a problem for me, I've been working through it until I got to this bit (which agrees with class mates - we all seem to be stuck at this point!)...

Im doing a differential equation and end up with my last step, which is an integration. I can't seem to remember how to integrate this one int. (tanx)/(1-cosx) hmmm [(sinx)/(cosx)] / (1-cosx) u = cosx du = -sinx dx throw a negative outside the integral...

Homework Statement find \int x^{\frac{3}{2}}\sqrt{1+x} dx Homework Equations The Attempt at a Solution Now i tried all the methods i know of which include integration by parts and substitution,the integration by parts didn't work too well, so substitution I tried. let...

First off, thanks for your help. I feel like a dope because everything I'm doing looks correct to me, but my answer is not the same as the book or solution manual gives! I'm usually so good at finding my mistakes. Thanks for taking the time to help. Homework Statement...

URGENT: Integrate exactly Homework Statement Using the substitution x = \sec ^2 u, evaluate \int_2^4 {\frac{{dx}}{{x^2 \sqrt {x - 1} }}} exactly 2. The attempt at a solution I have used the substitution and ended up with (after some simplification) \int_2^4 { - 2\cos ^2 u.\sin u.\sqrt...

Homework Statement Integrate the following: \int {3t^2 \left( {1 + t^3 } \right)^4 \,\,dt} Homework Equations \begin{array}{l} \int {\left( {a + bx} \right)^n \,\,dx = \frac{{\left( {a + bx} \right)^{n + 1} }}{{a\left( {n + 1} \right)}} + c} \\ \int {x^n \,\,dx =...

integrate the holy arcsine x :( Homework Statement The Integral arcsine (x) appears to be really problematic. I have to calculate the integral of sqrt(1-x^2). part of it is the arcsine x. Now I will ask only about arcsine x, and If any serious problem will occur i'll bother you with the...

Is it possible to intergrate e^x (cosx) i wondered because i tried to intergrate it by parts, but ended up going round in circles. I wondered because i had this question and I am stuck on how to do it :) http://img505.imageshack.us/img505/320/frfbc8.png

Nevermind sorry, think I've found a sufficent article on wikipedia to help me: http://en.wikipedia.org/wiki/Gaussian_integral

HELP, URGENT! how do i integrate (x)^1/3 how do i solve this? please help me integrate (X)^1/3

I am studying 'Integration' These are the questions I have been thinking of, but i still did not get it. 1.I understood the basic concept of dx and dy But I don't know what exactly does dx stand for in the definite and indefinite Integrals. \int x^3\, dx\right)2. I have read a proof in...

question in the attachment... integrate this function from 1 to 2. i can't find a way to do this quesiton it's from previous year final exam so there's no answer key to it.. hope someone would teach me.. thanks..

I've stared at this problem for about 5 minutes and I'm not sure how to start it. I see the function and its derivative, but I'm missing something I suspect is simple. Any suggestions as to how to start?

I need a little 'suggestion' as to how to integrate cos^6x sin^-3x dx. I rewrite to cos^6x/sin^3x dx and let u = sinx but when I'm trying to rewrite integral, what should I do with the ^6? Thanks!

Homework Statement Integrate the function e^(-x^2) with definite integrals -infinity to X Homework Equations The Attempt at a Solution I know that the indefinite integral of this reduces to sqrt(pi), but don't know what to do with the definite integral. Is this a known result...

Homework Statement I have to integrate (e^3lnx + e^3x)dx Homework Equations The Attempt at a Solution I have the answer and its (1/4)x^4 + (e^3x)/3 + C. I don't know how to get to the answer without the help of my calculator.