Substitution Definition and 797 Threads

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

i need to prove that if x is the first of sub(\phi;a,\psi) then there exists 1<=i<=n and there exist firsts \phi' of \phi_i and \psi' for \psi such that x=sub(\phi';a,\psi)\psi' where sub(t;a,b) is defined as follows: let a1,..,an be n signs and b1,..,bn expressions. a=(a1,...,an)...

How would I go about solving this: \int cos^2x tan^3xdx..all i did so far .. \int cos^2x tanx(tan^2x) [[ \frac{1}{cosx}^2 -1] = tan^2x so... \int cos^2x[[ \frac{1}{cosx}]^2-1]tanx is this right so far...now what?

Hi, I am having a little bit of trouble with the following: \int sintsec^2(cost)dt heres what I have so far u=cost du=-sintdt -\int sec^2(u)du -2tan(u) + C is this right?

I am working on a Differential Equation problem and I am stuck on these two integrals: http://forums.cramster.com/Answer-Board/Image/cramster-equation-20064101738436328028752372062504976.gif and...

\int \frac{dx}{5 - 3\sin x + 4 cos x} I know I have to use t = tan(x/2) substitution, and after i do that and symplify I get: \int \frac{dt}{2t^2 - 3t + 1} I don't know where to go from here. If anyone can see where to go, please help. Also, if there is an easier way to do this, please...

Hi there, I was given this equation, cosh(A+B)=cos(A).cosh(B) + sinh(A).sinh(B) then I was told to write down the definition of cosh(A+B) which I did. But then I'm told to substitue the defintions of cosh(A), sinh(A), cosh(B) and sinh(B) into the right hand side of the equation, and to...

Qn. By using a suitable substituition, find \int{\frac{1}{x\sqrt{1+x^n}}dx} I haven't encountered this specific type of question before, so I went to use the obvious substitution u^2=1+x^n, getting: 2u=n x^{n-1} \frac{dx}{du}\Leftrightarrow \frac{dx}{du}=\frac{2u}{n} x^{1-n} Hence...

Ok, in this problem I am getting bogged down in the basic algebra part of it. I had one person explain it once but I still missed something.:frown: a 1055-kg van, stopped at a traffic light, is hit directly in the rear by a 715-kg car traveling with a velocity of +2.26 m/s. Assume that the...

Am i being really dumb when struggling to do this? L = 4\sqrt{2}c \left \int_{0}^{\frac{\pi}{2}} \left \frac{dt}{\sqrt{1 + sin^2 t}} Using substitution or otherwise show that L = 4c \left \int_{0}^{1} \left \frac{du}{\sqrt{1 - u^4}} Its a small part of a question but its stopping me...

The question is to find the following intergal: \int x\cdot u^{\frac{1}{2} where u = 2x -1. = \int x\cdot u^{\frac{1}{2}} \;\; \frac{1}{2} du u = 2x -1 \Rightarrow x = \frac{u+1}{2} = \int \frac{1}{2}(u+1)\cdot u^{\frac{1}{2}} \;\; \frac{1}{2} du \;\; = \int \frac{1}{4}\left(...

I feel so :cry: doing this problem. PLEASE HELP! AND TEACH ME How TO DO IT. My question is this. use the substitution x=2tan(y) (37dx)/(x^2*sqrt(x^2+4)) give the answer in terms of y. I did the substition, but it looked more complicated. It doesn't look like a u*du thing, but it...

Hello! I've got a problem I've been working on for hours. I get a clue; If the integral (from zero to infinity) of e^(-x^2) is sqrt(pi)/2, what is the integral (from zero to infinity) of e^(-bx^2)? I've tried substitution, but I kind of got it wrong. If x = y/sqrt(b), I get the same...

Solve the differential equation by making an appropriate substitution x^2dy=(xy+x^2e^\frac{y}{x}) Here was my first attempt: Let y=ux, dy=udx+xdu x^2(udx+xdu)=(ux^2+x^2e^\frac{ux}{x})dx x^2(udx+xdu)=(ux^2+x^2e^u)dx x^2udx+x^3du=x^2udx+x^2dx+e^udx x^3du=x^2dx+e^udx And after...

I am not too good with trig identities. I can't seem to figure out how to simplify these trig intergrals. I know I can use a triangle to turn the second problem into a trig integral, but once I have the trig integral, I am lost. Any help would be greatly appriciated.:redface...

Ok, apparently it's been a while since I've had to deal with an integral like this, seems like it should be easy but I can't find a substitution that will work. The integral is: \int_{0}^{h}\frac{dx}{(x^2+R^2)^\left1/2\right} Where R is a constant. Any hints (or solutions if you're...

my question is integra 1 / x^2 sqr root(16-x^2) i use x = 4 sin y then i got to integrate 1/16 times [1/(sin y)^2] in which i got stuck.pls help...how do i continue from there as i not sure ow to integra 1/(siny^2

how would on integrate \int_{0}^{1} \sqrt{1 + 4t^2} dt trig sub sittution doesn't work since one doesn't get tan^2 +1 . i tryed solving this with matematica and it yielded something with a sinh argument. I am not familiarwi the hyp sine substitution.