Substitution Definition and 816 Threads

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...

Homework Statement prove by substitution that definite integral int (1/t)dt from [x to x*y] = int (1/t)dt from [1 to y]. Homework Equations The Attempt at a Solution i can do this problem if i integrate and use the log laws, no probs, but the question says to use a substitution...

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?

int^{0}_{t}[cos(sqrt{x}]dx can anyone tell me the solution to this question !

I'm not sure about answer.It looks very strange. Homework Statement \int_{1}^{e}\frac{dx}{x\sqrt{1+ln^2x}} The Attempt at a Solution for u=lnx-->u'=1/x \int \frac{du}{\sqrt{1+u^2}} substituting u=tan\theta =\int \frac{d\theta}{cos\theta}=ln|sec\theta+tan\theta|...

[SOLVED] trig substitution This is from the class notes. Evaluate the integral: \int_{}^{} {\frac{x}{{\sqrt {3 - x^4 } }}dx} \begin{array}{l} u = x^2 ,\,\,du = 2x\,dx\,\, \Leftrightarrow \,\,dx = \frac{{du}}{{2x}} \\ \\ \int_{}^{} {\frac{{x^1 }}{{\sqrt {3 - x^4 } }}dx} =...

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...

This is an example from the book. Evaluate \int {\frac{{\sqrt {9 - x^2 } }}{{x^2 }}dx} I understand all the steps that get me up to = - \cos \theta \, - \theta \, + C Then the book goes on to explain: "Since this is an indefinate integral, we must return to the original variable...

Homework Statement Can anybody help me integrate x^3 e^{x^2} The Attempt at a Solution I can't see how to do it by substitution or integration by parts.

\int \frac{x^2}{\sqrt{9-x^2}} find the integral using trig sub x= 3 \sin {\phi} replace 3sin\phi into x and solve. I got to \int \frac{9-9 \cos{\phi}}{3 \cos{\phi}} then what should I do?

\int\sqrt{16-(2x)^{4}}xdx Hint says you may like to use the identity sin(theta)cos(theta)= sin(2theta)/2 However, I think I found a way to use 1-sin^2(theta)=cos^2(theta) First, (2x)^4 = 16x^4 So make it 16(1-x^2)^2. Take the 16 out of the root and the integral and you have...

Homework Statement {\int_{}^{}}{ \frac{ds}{{({s}^{2}+{d}^{2})}^{\frac{3}{2}}}} s \equiv variable d \equiv constant Homework Equations u-substitution techniques for integration. The Attempt at a Solution This integral is particularly tricky as I have already made several...

[SOLVED] Integration By Parts and Substitution Short background; Took Calc 1 my senior year in high school. Got As all 4 quarters and found it quite easy. Freshman year comes around and I sign up for Calc 2. Turns out the only teacher teaching Calculus 2 for my fall and spring semester is a...

Homework Statement Prove \int_0^{1} \frac{1}{\sqrt{x^2+6x+25}} = ln(\frac{1+\sqrt{2}}{2})Homework Equations The Attempt at a Solution \int_0^{1} \frac{1}{\sqrt{x^2+6x+25}} = \int_0^{1} \frac{1}{\sqrt{(x+3)^2+16}} Let x+3=4tan\theta so that dx=4sec^2\theta d\theta and so the problem becomes...

So I have another U substitution. \int sec^3(2x)tan(2x) this one is a little tricky for me. I have tried letting u= sec2x and tanx and 2x. 2x definitley gets me nowhere. I may be mistaken on the others. I will recheck them. I was also thinking of rewriting it as \int sec^4(2x)sin(2x)...

I know this must be similar... \int \frac{e^x}{1+e^{2x}} should u=1+e^{2x}? Casey

[SOLVED] Integration, u substitution, 1/u -- +C at the end of the integral solutions, I can't seem to add it in the LaTeX thing -- Homework Statement #1 \int\frac{1}{8-4x}dx #2 \int\frac{1}{2x}dx The Attempt at a Solution #1 Rewrite algebraically: \int\frac{1}{x-2}*\frac{-1}{4}dx Pull out...

Homework Statement /int (2t+4)^-1/2 dt. the answer is 2(sqrt3)-2 Homework Equations The Attempt at a Solution u^-1/2*(1/2)du (-1/2)(u^1/2) (-1/4)(2t+4)^1/2 (-1/4)(sqrt 12)= (-1/4)(4(sqrt 3)/1)=sqrt 3 (sqrt 3)-1/2 2(sqrt 3)-1

The benzene are sulphonated using acid sufuric. Please show me how the substitution happened as i really don't see how SO3H can attached to the benzene group and how the SO3H are separated from H2SO4. I really need to understand this substitution.. Thanks

Homework Statement Evaluate ∫ x √ 4 + x2 dx by using the trigonometric substitution x = 2tanθ I am starting on the right track by subbing x=2tanθ into x like this: =∫ 2tanθ √ 4 + 2tanθ(2) then, do I just integrate that for the correct answer?

Using the substitution u=1/x, evaluate: \int {\frac{{dx}}{{x^2 \sqrt {1 - x^2 } }}} I was able to do it making the substitution x=cos\theta, but I am supposed to show a worked solution using the given substitution. \int {\frac{{dx}}{{x^2 \sqrt {1 - x^2 } }}} = \int {\frac{{ - x^2...

\int_{-2} ^2 \frac{dx}{4+x^2} I use the trig substitution and get everything done but for some reason I can't get the answer, here's all my working: x = 2 \tan\theta dx = 2 \sec^2\theta 4+x^2=4(1+\tan\theta)=4\sec^2\theta \int \frac{2\sec^2\theta d\theta}{4\sec^2\theta} \int...

Homework Statement I have this function F(r)=\frac{(r-r_+)(r-r_-)}{r^2} and I want to make the subsitution r=r_+(1+\rho^2). Homework Equations None. The Attempt at a Solution So, I sub in, to obtain...

Homework Statement (Idk how to put in the equation to make sense, therefore it is at the link below) Homework Equations The Attempt at a Solution Here is all I have done. Something just isn't right...there should be 3 answers (in the back of the book) because there is a cube...

Can someone please explain the Substitution Rule to me in easier terms? I am soooo confused! Thanks, Allison

Homework Statement how would one calculate 4 \int_0^{\frac{\pi}{2}} \frac{\cos^2 \theta}{(1 + \cos^2 \theta)^2} d \theta ? The Attempt at a Solution someone suggested a u = \tan \theta substitution, but i don't understand why and how this would help me. couldn't i just use u = \cos t?

The question is to evaluate the integral in the attachment. Using trig substition, I've reduced it to ∫ (tanz)^2 where z will be found using the triangle. I just need to integrate tangent squared which I can't seem to figure how to do. I tried using the trig identity (secx)^2 - 1 but I don't...

Out of curiosity there are several trig functions that can be integrated (WITHOUT the use of trig identities) using Integration by Substitution. One particular example is this: sin(x)cos(x) dx Integrating this with substitution u = cos(x) works out fine. HOWEVER integrating with...

You remember the substitution rule (or Change of variables theorem), when the integrand is some real function of real variable. I would like to know if that rule has a version when the integrand is some vectorial function (of real variable). Thanks for your attention.

Homework Statement \int\frac{dx}{\sqrt{x^2 + 16}}Homework Equations x = 4\tan\theta dx = 4\sec^2\theta \ d\thetaThe Attempt at a Solution \int\frac{4\sec^2\theta}{\sqrt{16\tan^2\theta + 16}}\ d\theta \int\frac{4\sec^2\theta}{\sqrt{16(\tan^2\theta + 1)}}\ d\theta...

Homework Statement The equation of motion of a mass m relative to a rotating coordinate system is m\frac{d^{2}r}{dt^2} = \vec{F} - m\vec{\omega} \times (\vec{\omega} \times \vec{r}) - 2m(\vec{\omega} \times \frac{d\vec{r}}{dt}) - m(\frac{d\vec{\omega}}{dt} \times \vec{r}) Consider the case F =...

Homework Statement Evaluate the following integrals or state that they diverge. Use proper notation. Integral from 0 to 2 of (x+1)/Square root(4-x^2) Homework Equations The Attempt at a Solution I just substituted x = 2sin(theta) thus dx = 2cos(theta) I got to the...

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...

Homework Statement Homework Equations The Attempt at a Solution I'm not asking for someone to do the question for me but I was just wondering what I'm supposed to sub in. Do I put in as if it was (x^2-9)^(1/2) or do I have to do something differently if there is a constant in front...

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

Homework Statement \int {\sec ^3 x\,\,\tan x\,\,dx} Homework Equations u = \sec x This is my guess at u. The Attempt at a Solution \frac{{du}}{{dx}} = \sec x\,\,\tan x,\,\,\,dx = \frac{{du}}{{\sec x\,\,\tan x}} \int {\sec ^3 x\,\,\tan x\,\,dx} = \int {u^3...

I really don't get the substitution rule. This is supposed to be the easiest problem in the homework set: u=3x \int {\cos \,3x\,\,dx\,\, = \,\,\int {\cos \,u\,\, = \,\,\sin \,u + C\,\, = \,\,\sin 3x + C} } But the right answer is 1/3 sin(3x). Where did the 1/3 come from?

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...

Hi! I am looking through some solved exercises. One of them is the following: Solve the equation: x^2 y'' + (x^2 - 3x)y' + (3-x)y = x^4 knowing that y=x is a solution of the homogeneous equation. The professor then solves it by doing the following substitution: y=xz. Then he...

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)

1) Predict the relative reaction times from fastest to slowest for the following compounds with NaI in acetone: 1-chlorobutane, 1-bromobutane, 2-chlorobutane. I am assuming that this is under SN2 reaction conditions with the solvent and compound given. 2-chlorobutane = secondary...

I'm really stomped with this problem... i can't seem to get the answer... anyway... here's the problem.. (2(x^3) - (y^3))y'=3(x^2)y and i need to get the general solution... SO, here's what i did... I Let u=x^3 and du=3x^2dx so what happens is 2udy-(y^3)dy= ydu and...

The bit of the problem that I'm working on: 6\int\frac{dx}{x^2-x+1} My work: =6\int\frac{dx}{(x^2-x+\frac{1}{4})+1-\frac{3}{4}} =6\int\frac{dx}{(x-\frac{1}{2})^2+\sqrt{\frac{3}{4}}^2} let x-\frac{1}{2}=\sqrt{\frac{3}{4}}\tan\theta so dx=\sqrt{\frac{3}{4}}\sec^2\theta d\theta...

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...

evaluate the indefinite integral ((e^x)/((e^x)+1))dx I let u = ((e^x)+1) then du = (e^x)dx which occurs in the original equation so.. indefinite ingegral ((u^-1)du) taking the antiderivative I get 1 + C is this right? thanks!

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

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-

There is a problem in my book which wants us to find the general solution to the given equation. I understand most of the problem it is just the integral part that is tricky. Here is the problem: x(x+y)y' = y(x-y) In this problem I know that you need to divide the equation by x and you...

I am having real trouble with this second order differential The substitution is given and i just can't seem to use it What am i missing here? x \frac{d^2 y} {dx^2} -2 \frac{dy} {dx} + x = 0, \frac{dy} {dx} = v All help welcome