Integration by substitution Definition and 86 Threads

Homework Statement If f is continuous and \int^{9}_{0}f(x)dx = 4, find \int^{3}_{0}xf(x^{2})dx Homework Equations None required The Attempt at a Solution Don't really know where to begin, but I tried: for \int^{3}_{0}xf(x^{2})dx let: u = x^{2} du = 2xdx substitute...

Hi, am I on the right track with this U-substitution problem? Homework Statement Evaluate the indefinite integral Homework Equations integral of x^2(x^3 + 5)^9 dx The Attempt at a Solution integral of x^2(x^3 + 5)^9 dx Let u = x^3 + 5 du = 2x^2 1/2du = x^2 1/2 integral u^9 du 1/2...

Homework Statement Question is:Integrate x(2x+1)^8 dx in terms of x. Homework Equations The Attempt at a Solution Here is how i started off:by relabeling them. let u = 2x+1. du/dx = 2. dx=du/2. Also x=u-1/2. So my terms now are: Integral (u-1/2)u^8 (du/2) <- this is where i...

Homework Statement 2 h(x)=∫√(1+t^3) dt find h'(2) x^2 Homework Equations The Attempt at a Solution I started out solving this equation by flipping x^2 and 2 and making the integral negative. From here on out, I'm lost. I've tried substituting u in for 1+t^3 and solving...

Homework Statement Compute the indefinite integral. ∫(x^2 + 1)^(-5/2) dx The Attempt at a Solution I have a hunch that I need to substitute x = tan(u) but, as always, my lack of trig skills are holding me back.

Homework Statement \int sin^{5}x cosx dx Homework Equations None The Attempt at a Solution I tried setting u=sin^5(x) but this ended up yielding \frac{1}{5}\int u cos^{3}x du and I cannot think of a better substitution. Any tips?

Homework Statement Integrate \int\frac{dz}{1+e^z} by substitution Homework Equations The Attempt at a Solution I chose u=(1+e^{z}) so du/dz=e^{z} and dz=du/e^{z}. Therefore, \int\frac{1}{u} \frac{du}{e^{z}} I plug z=ln(u-1) in for z, so \int\frac{1}{u} \frac{du}{u-1}...

Homework Statement I was asked to find the formula for the antiderivative \int1/(25+x^{2}) Homework Equations Take a 'part' of the equation and use it to solve the antiderivative, integration by substitution. and dw=(1/5)dx The Attempt at a Solution I initially set my substitution...

Homework Statement I've come across the problem \ \int x(x^{2}+5)^{75} dx Homework Equations The Attempt at a Solution Once going through the whole problem I got \ \frac{(x^{2}+5)^{76}}{76}+c but the text I have said the answer was, \frac{1}{152}(x^{2}+5)^{76}+c. What did I do...

Homework Statement I have the function below which i need to find the area under the graph. Homework Equations \int_{ - \frac {\pi}{4}}^{\frac {\pi}{3}}\frac {2\sec x}{2 + \tan x}dx The Attempt at a Solution I can simplify it to \int_{ - \frac {\pi}{4}}^{\frac {\pi}{3}}\frac {2}{2\cos x +...

Homework Statement Use substitution to evaluate the integral. \int \frac{4cos(t)}{(2+sin(t))^2}dt Homework Equations None, really.The Attempt at a Solution I'm not sure what to use as u, for the substitution. I've tried (2+sin(t))^2, as well as other attempts, but I can't seem to find anything.

Homework Statement It's been god knows how long since I've had to use integration by substitution. I've totally forgotten it. I am trying to integrate to solve for the value of an electric field at a given point. The integral I am trying to solve is...

1. Homework Statement : using the substitution u=3x+4, work out: \int 2x \sqrt{3x+4}2. The attempt at a solution: \int 2x \sqrt{3x+4} u=3x+4 \rightarrow \mathrm{d}x = \frac{\mathrm{d}u}{3} \int \left( \frac{u-4}{3} \right)\left(u^{\frac12}\right) \ \frac{\mathrm{d}u}{3} \frac19 \int u^{\frac32}...

I just learned how to integrate through substitution and I was challenged by my teacher with an apparently easy problem but I'm really struggling with it. He said he will give me an F if I don't solve it for tomorrow, I guess this is what I get by being the one who always understand in class...

Homework Statement Evaluate the definate integral of the following \int (from 1 to 2) \frac{sin t}{t} dt The Attempt at a Solution I am actually stuch from the very beginning. I tried to set u=sin(t) but this doesn't help much because (sint)'=cost and this is going to make the...

Hello all, how are you? we are currently working on integration by substitution, what do you guys think about the way i solved this one: Find: \int \frac{(t+1)^2}{t^2} dt My solution: \int \frac{(t+1)^2}{t^2} dt = \int 1dt + \int \frac{2}{t} dt + \int \frac{1}{t^2} dt = t +...

Homework Statement I want to integrate (1+x)/(1-x) Homework Equations The Attempt at a Solution I have looked at many examples of substitution method - this one appears simple but I am not finishing the last step... - I know you must first take u=(1-x) - Then du = -dx what...

1. Find, by substitution, the integral of; 3x2(x3 - 2)4 dx 2. susbt' 3. u = x3 - 2, so du/dx = 3x2, and du = 3x2 dx Now this is where I'm not sure what to do. As u = x3 - 2 you know that x = (u + 3)1/3, and so i think you can write the integral as; \int(u+3)1/3.u4 du ... but i when i look...

Hi all, I've been studying calculus out of Tom Apostol's book "Calculus". I'm having troube with the following problem in the section on integration by substitution: Integrate \int(x^2+1)^{-3/2}\,dx. I tried the substitution u=x^2+1 but it didn't seem to work. I can't see anything else...

Question: \int^{1}_{-1} \frac{dx}{(1+x^4)} I attempt: u = x^2, so x= u^1/2 dx= 1/2 u^(-1/2) Which gives me \int^{1}_{1} \frac{1}{(1+x^4)} * \frac{1}{(2u^1/2)}du, which is 0. Thats not the answer as seen by any graphing utility. Where is this error? I do not know integration by parts. I just...

the problem asks for the area under the shaded region of the line y = 1/(1-x^2) on the interval [-1,1]. so far I've set up the integral showing \int [tex]dx/(1-x^2)[\tex] on the interval [-1,1] i'm pretty sure you have to use substitution to solve it, but i can't seem to figure it out...

How was Integration by Substitution and Trig Substitution developed? My calc book doesn't have much info, just a short (not really complete) proof. Could someone explain and/or lead me in the right direction?

Homework Statement Homework Equations None. Well, dx=du/cosx The Attempt at a Solution I've substituted it in, got new values for the limits but I have u^-1 on the bottom and so can't integrate it from my current knowledge. Basically I'm stuck with: Integration of u^(-1) du...

Homework Statement Find by letting U^2=(4 + x^2) the following \int_0^2\frac{x}{\sqrt{4 + x^2}}dx? I can solve it by letting \mbox{x=2} tan(\theta), But I want to be able to do it by substitution. The Attempt at a Solution...

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

Homework Statement Solve the differential equation. dy/dx = 4x + 4x/square root of (16-x^2) Homework Equations Substituting using U... The Attempt at a Solution I'm not sure if that's what I am supposed to do, but I tried using the U substitution... 4x + 4x/square root of...

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)

Hello, evaluate the following integral: \int x \sqrt{x^2+a^2}dx definite integral from 0 to a what I did was u = x^2 + a^2 du = 2xdx 1/2 sqrt(u)du I just dropped the a^2 because we were finding the derivative of x but feel that it's very wrong.Any suggestions are much appreciated. thanks.

evaluat the indefinite integral ((sin(x))/(1+cos^2(x)))dx I let u = 1 + cos^2(x) then du = -sin^2(x)dx I rewrite the integral to - integral sqrt(du)/u can I set it up like this? should I change u to something else? I also tried it like this by rewriting the original equation...

Definite integration by substitution I just need a check on this, the book and I are getting different answers... The problem and my answer: http://www.mcschell.com/p14.gif http://www.mcschell.com/p14_worked.jpg The book gives 0.00448438 though. :confused: Thanks! -GeoMike-

I am going crazy on this problem: \int sec(v+(\pi/2)) tan(v+\pi/2)) dv if I substitute u= tan(v+\pi/2)) dv , can I use the product rule to find du= sec(v+(\pi/2)) dv . Thanks, Todd

I'm stuck on how to advance further on this problem and if anyone can point my in the right direction I would be greatly appreciative. \int\frac{dx}{\sqrt{x(1-x)}} The integral has to be solved using substitution, but we are required to use u=\sqrt{x} From this...

Integration by substitution... Accroding to my notes, when performing integration by substitution, du/dx= f'(x), and therefore du = f'(x)*dx. But how is this possible? We are treatnig dy/dx as if it were a fraction - but in essence it is not! So why is this statement still true? Thanks. :smile:

Please help. I'm having trouble with a simple integration by substitution problem The integrand is f(x) = x* sqr(x-1) The interval [1,2] Please draw it out in a gif file and send it to me via email. -much appreciated.

For our homework this week for Pure, one of the questions is to ingration 1/(16 + x^2) with respect to x between the limits 0 and 4. I know the result from the formula wqith arctan in it, but since we've to use substitituion here and not just plonk down the formula, I'm confused as to what to...

How do you do this question, I've spent hours figuring it out: Use the substitution x = 3sint to show that 3 [inte]x^2[squ](9-x^2) dx = (81/16)pi 0