Substitution Definition and 797 Threads

Homework Statement Hey folks, I think I know how to solve this by parts but I need a substitution to get there. I've been staring at examples for a while but I still don't understand how to apply the substitution rule. Anyway, here's the integral: \int x^9cos(x^5) Homework Equations...

Homework Statement Integral ( cos(x)/(1+cos(x))^.5 dx) Homework Equations The Attempt at a Solution Integral ( cos(x)/(1+cos(x))^.5 dx) Square it Integral ( cos(x)^2/(1+cos(x) dx) Multiply by the Conjugate Integral ( cos(x)^2/(1+cos(x) * (1 - cos(x))/(1 - cos(x)) dx)...

http://www.math.cmu.edu/~handron/21_122/hw/hw1.pdf My question is about number 5.5.64 on that page. "If f is continuous on R, prove that ..." I have been unable to do this and would appreciate help.

Homework Statement I have these compounds, and I have to predict which one will undergo unimolecular substitution reaction the fastest. And which one will undergo it the slowest. 3 bromo cyclohexene 1 bromo cyclohexene 4 bromo cyclohexene 2 bromo hexane (not cyclohexane/ene) The...

Homework Statement verify by direct substitution that the wave function for a standing wave given in equation below is a solution to the general linear wave equatin. y= (2A sin kx)cos \omega t \frac{\delta^2y} {\delta x^2}= \frac{1} {v^2} \frac{\delta^2 y} {\delta t^2} Homework...

Homework Statement Ok, so I was doing a problem on the electric field strength of a continuous charge distribution and I arrived at this seemingly easy integral \int \frac{1}{({l^2+a^2})^\frac{3}{2}} dl sorry the latex is lagging badly, you can see the correct integral by clicking on it. it...

Have this question in relation to some investment exam I am doing, I am a maths novice being some years since leaving school etc, ok enough of the excuses. Example FV = future value PV = present value R = interest rate N = number of compounding periods my PV is 6000 and my FV is...

[SOLVED] Integration with Trigonometric Substitution Homework Statement Given integral (I): I[(x)sqrt(9-x^2)dx] by words: Integral of "X" times square root of "9-X(squared) Use proper trigonometric substitution to solve this problem. Homework Equations The Attempt at a Solution

I have a few quick problems concering evaluating integrals by trigonometric substitution. I guess I will just post five that way if anyone can help with any, would be greatly appreciated. Also: if anyone could inform me on how to input the actual equations onto this forum as I have seen in some...

So if we have, say, a polynomial f(x) = a_n x^n + ... + a_0 and, say, use the substitution x = y + a, then do ALL irreducibility tests work the same? And do all OTHER tests also work the same? Is the polynomial FUNDAMENTALLY the same? And what theorem is there to prove this?

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...

how would i start this solution off? we replace 7.5 atomic % of the chromium atoms in its BCC crystal with tantalum. X ray diffraction shows that the lattice parameter is 0.29158 nm find the density.

Homework Statement Solve by making an appropriate substitution. I am given the homogeneous DE:xdx+(y-2x)dy=0 Now we have bee using either y=ux or x=vy. . . I tried both, but the latter seemed easier. x\frac{dx}{dy}+y-2x=0 letting x=vy and dx/dy=v+y*dy/dv vy(v+y\frac{dy}{dv})+y-2vy=0...

[SOLVED] Free fall far away from Earth (integral substitution problem) Homework Statement Given: v(x) = -v_1\sqrt{\left(\frac{R}{x} - \frac{R}{h}\right)} Find the time t. Homework Equations Listed above where v_1 , R , h are all constant. The Attempt at a Solution v(x) =...

Homework Statement Use the substitution x=4sin(t) to evaluate the integral: S 1/[(16-x^2)^(3/2)] dxHomework Equations x = 4sin(t) The Attempt at a Solution x = 4sin(t) dx = 4cos(t) dt 4cos(t) = (16-x^2)^(1/2), i cube both sides to get (4cos(t))^3 = (16-x^2)^(3/2), then plug in dx and...

Homework Statement Use substitution to evaluate the integral Homework Equations ∫√(cotx) csc^(2)x dx?

Homework Statement \int \frac{cosx dx}{\sqrt{1 + sin^{2}x}} Homework Equations Expression: \sqrt{a^{2} + x^{2}} Substitution: x = a*tan\Theta Identity: 1 + tan^{2}\Theta = sec^{2}\Theta The Attempt at a Solution I have tried using Trig Substitution, but I end up getting an equation much...

Homework Statement \int ((sin(x))^3/(cos(x)) )*dx The Attempt at a Solution alright i have been trying to use u= cosx -du = sinx but it doesn't make sense bause there is still a sinx^2 to account for so i know i need to make a trig substitution but i can't figure out the appropriate...

[SOLVED] More trig substitution help... I've looked at this problem about 3 times and still can't figure it out...where identity did they use to substitute out the part in the red box? Thanks for the help

Homework Statement Find the indefinite integral. The antiderivative or the integral of (x^2-1)/(x^2-1)^(1/2)dx Homework Equations The Attempt at a Solution Tried using (x^2-1)^(1/2) as u and udu for dx and I solved for x but I am still left with a 1 on top not sure how to...

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 Using transforms: u = 3x + 2y and v = x+4y solve: \iint_\textrm{R}(3x^2 + 14xy +8y^2)\,dx\,dy For the region R in the first quadrant bounded by the lines: y = -(3/2)x +1 y = -(3/2)x +3 y = -(1/2)x y = -(1/2)x +1 I'm itching to see where I've gone wrong on this one...

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...

Homework Statement \int1/[Sin[x]\sqrt{}((Sin[x])^2+k)] The Attempt at a Solution I don't have any idea of the solution. Mathematica gives the answer as -(1/sqrt(k))ArcTanh[(Sqrt(2k)Cos(x))/sqrt(1+2k-cos(2x)]

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...

Homework Statement \int \frac{1}{1+\sqrt{2x}}dx Homework Equations u=1+\sqrt{2x} \sqrt{2x}=u-1 dx=(u-1)du The Attempt at a Solution I was able to get it down to: \int (1-\frac{1}{u})du = u-\ln{lul}}+C = 1+\sqrt{2x}-\ln{l1+\sqrt{2x}l}+C However, my book says that...

For the integral \int frac{x^3}{sqrt{1-x^2}} dx} ==> okay... what I meant was: int of x^3 over sqrt(1-x^2) --I trig substitute to get sin^(3)(x)cosxdx over cos x and end up with sin^3(x)...this is obviously wrong, can anyone point out what i did wrong?

Homework Statement 1) antiderivative of ((t^2)+2)/((t^3)+6t+3) dt 2) antiderivative of r(sqrt((r^2)+2))dr help please with these Homework Equations The Attempt at a Solution #2 let u = r^2 + 2 du/dr = 2r du = 2rdr?? i don't knoww!

[SOLVED] Integrating substitution problem? Homework Statement Sorry to hijack this thread sort of (as a similar named one already exists), but the title is aptly suited to my question. I have integral to integrete and I don't really know how to do it tbh. . . s=\int{\sqrt{2+(3t)^2}dt...

[SOLVED] Integration using substitution Problem: Find the integral of: \int\sin^{6}\theta\cos\theta d\theta My attempt: Let u\equiv\cos\theta so: du\equiv\sin\thetad\theta Only I don't know where to go from there. The book says it should \frac{1}{7}\sin^{7}\theta+C but I have no idea how...

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...

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}} [SIZE="4"] 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...