Substitution Definition and 797 Threads

Homework Statement ∫xtan^-1(x^2)dx Homework Equations The Attempt at a Solution I did u = x, du = 1, v = ? ,dv = tan^-1(x^2)dx I do not know how to get the integral of tan^-1(x^2)

Homework Statement Making sure I got the right answer.Homework Equations The Attempt at a Solution

Homework Statement integral (1)/(x^2sqrt(36-x^2) Homework Equations The Attempt at a Solution I found X=6sinθ dx=6cos √(36-x^2)=√(36-sin^2θ)=6cosθ i think the problem is that i am not getting integral of ∫csc^2θ

Homework Statement integral of dx/((9-(x^2))^(3/2)) A = 0, B = 3/2 Homework Equations Trigonometry Substitutions 3. The Attempt at a Solution : I am stuck with this question. So far, I got (1/9)integral of (1/cos^2(θ)) dθ

If I had an integral \int_{-1}^{1}e^{x}dx Then performing the substitution x=\frac{1}{t} would give me \int_{-1}^{1}-e^\frac{1}{t}t^{-2}dt Which can't be right because the number in the integral is always negative. Is this substitution not correct? Sorry if I am being very thick but I...

Homework Statement I am given an integral for which I need to substitute variables to remove a singularity so that the integral can be computed in Matlab using the Composite Trapezoidal Method, and then compared to the integral computed in Maple to 16 digit precision. I am stuck on the variable...

What is the easiest way to take the integral of: [SIZE="4"]\int[SIZE="3"]\frac{(6+e^{x})^{2}dx}{e^{x}} I have been having quite some difficulties with this one but here is my work so far: Let u=e^{x}, du=e^{x}dx =[SIZE="4"]\int[SIZE="3"]\frac{(u+6)^{2}du}{u^{2}} Then let s=u+6 ∴ u=s-6...

The problem statement Evaluate the indefinite integral ∫\frac{\sqrt{x}}{\sqrt{x}-3}dx The attempt at a solution My first thought was to substitute u for √(x)-3, but then du would equal \frac{1}{2\sqrt{x}}dx, and there's no multiple of du in the integrand. Next, I tried splitting up...

I am unsure whether I have properly performed the integration of the integral ∫((sin(√x))^3*dx)/√x When I used my TI-Nsprire CAS to take the derivative of my answer in order to check if I was correct, and it came out differently. Now I used some trig identities to manipulate the problem, so I...

Homework Statement evaluate the definite integral ∫(0 to 3) dx/sqrt(25+x^2) Homework Equations The Attempt at a Solution I first used substitution and set x=5tanθ, and dx=5tanθsecθdθ then i wrote the integral as 5∫ tanθsecθdθ/sqrt(25(1+tan^2(θ)) after some simplification i...

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

Homework Statement Find the following integral ∫1/(x*sqrt(x^2-1) dx Homework Equations The Attempt at a Solution I've decided to use the substitution: x = sec u dx = sec u * tan u du Substituting on the integral I got: ∫sec(u)*tan(u) / [sec u * sqrt((sec^2(u)-1))]...

I put it in std form, did the homogeneous test. it passed with degree 2. I substituted y=ux and dy=udx+xdu and now I'm stuck. it needs to be simplified somehow but I don't know if ux is one var or if it's u*x. Same goes for udx and xdu. Is it really u*dx+x*du? even assuming that is correct, it...

Homework Statement \int_{-p}^{p} \frac{2p}{(1+v^2)\sqrt{p^2 + v^2 +1 }} dv Homework Equations 1 + \tan{\theta}^2 = \sec{\theta}^2 The Attempt at a Solution I thought the best way to go about this was to rename some constants. Let \alpha^2 = 1 + p^2 so that we are left with...

If we see the form \sqrt { { a }^{ 2 }-{ x }^{ 2 } }, we always set x=asinθ How do we know that it will work in advance? Just trial & error?

It's been a year since I took Calc I, and I'm taking Calc II online this semester. This is technically a review problem from Calc I, and I managed the other seven, but I can't figure out how to solve this problem. 1.a Homework Statement ∫(a*sin(14x))/(\sqrt{1-196x^2} dx, evaluated at x=0...

Homework Statement I do not know how to solve the following indefinite integral. I personally think it is very difficult and would appreciate it had someone can explain it step by step? Homework Equations / The Attempt at a Solution This integral must been solved by mix of...

Homework Statement http://i.imgur.com/d0EKw.png Initigral (x* dx/((1+x^2)^.5) substitution u = 1+x^2 du = 2xdx how do get this to equal the inigral of U^-1/2 I am drawing a blank for the numerator I know how do the problem after I get u^-1/2 .. but i need to know how to get...

[FONT=arial]Studying for finals here...So I have this specific problem to use trig substitution on. $$\int \frac{x^2}{\sqrt{1-x^2}}\,dx$$ I begin by substituting $$x={sin{\theta}}$$ I am fine with doing everything up to the point where I have an answer for the integral in terms of...

Hi, I want to solve an overdetermined non-linear equation with the method of least squares. Assume it's f(x) = 1 + ax + a^2 + b, and I want to estimate a and b. This is non-linear, as I said, so the derivatives of the squared residuals involve a^3 terms and are difficult to solve. Now I thought...

Homework Statement 5a = 5 - b 5a = 3 - b Homework Equations The Attempt at a Solution I got the solution set to be 1/2, 5/2 i used substitution for substituting a into b of the second equation, just like they were x's and y's just used a's and b's there is no difference...

Homework Statement Integrate -1/(1+x(sin(t))^2) between 0 and pi/2 using the substitution u = tan(t)The Attempt at a Solution du/dt = (sec(t))^2 dt/du = 1/(1+u^2) I've messed around with the integral and trig. identities but I don't seem to be getting anywhere changing the integral to make...

Homework Statement I have four equations and have four variables. I need to solve for each of the variables. I am having difficulty figuring out how to do this. My equations are here. http://imgur.com/EOA8I Homework Equations \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1 The Attempt...

Hi guys... I'm probably missing something pretty basic here but I can't seem to figure this out. I was working on a problem recently: for the complex functions f(z)=ez and g(z)=z, find their intersections. This post is not about the problem, it is about something I noticed while tackling it...

I have a problem with Double Integral that I can not seem to get correct. 4 2 ∫ ∫ e^(y^2)dydx 0 (x/2) The answer is (e^4)-1, but I can't seem to get the Substitution at all right. I have literally spent hours on this problem. Any help would be greatly appreciated, its...

Homework Statement I'm stuck at an attempt to solve an integration step. I think I'm supposed to trig substitute? Homework Equations http://img685.imageshack.us/img685/9158/unavngivetn.png It is the second to third equation I'm having a hard time with The Attempt at a Solution From second...

integration by parts I'm working through Apostol's Calculus. I have attached the problem. I need to derive the formula integrating by parts. It is not a hard problem, but I can't seem to understand how on Earth the author came up with that expression. I take f(x) = (a^2 - x^2)^n, so...

Homework Statement Show that y(t) = (1/w) ∫[0,t] f(s)*sin(w(t-s)) ds is a particular solution to y'' +w2 y = f(t)where w is a constant. The Attempt at a Solution After wasting several pages of paper I have made virtually no progress. Obviously, substitution suggests you plug in y(t)...

μ^{2}\frac{d^{2}u}{dx^{2}}+ae^{u}=0 Boundary conditions: u(-L)=u(L)=u_{0} Solve by multiplying by \frac{du}{dx} and integrating in x I know you have to use substitution, but I keep going in circles.

Homework Statement From Larson, 9th Edition: Section 4.5. Solve the differential equation \frac{\operatorname{d}y}{\operatorname{d}x}=4x+ \frac{4x}{\sqrt{16-x^2}}Homework Equations The Attempt at a Solution Well, I can get my book's answer, but not through doing things in the prescribed way...

Homework Statement use the substitution u= x+y and v=y-2x to evaluate double integral from ∫1-0∫(1−x) -(0) of (√x+y) (y−2x)^2 dydx Homework Equations integration tables I am assuming The Attempt at a Solution i tried to integrate directly but none of my integration tables match...

Hi! I am currently working with a linear PDE on the form \frac{\partial f}{\partial t} + A(v^2 - v_r^2)\frac{\partial f}{\partial \phi} + B\cos(\phi)\frac{\partial f}{\partial v} = 0. A and B are constants. I wish to find a clever coordinate substitution that simplifies, or maybe even...

We have a gravitational force on Planet X F=mγy^2 and we want to know the particle's final velocity. I know how to get the right answer, but I am wondering how come this doesn't work. F = mγy^2 ma = mγy^2 ∫a dt= γ∫y^2 dt Integral from 0 to t, I take v_0 = 0 y_0=0 v = γy^3/3

Homework Statement By using substitution u=\frac{1}{t}, or otherwise, show that \int^∞_1 \frac{t^5}{(1+t^3)^3}dt=\int^1_0 \frac{u^2}{(1+u^3)^3}du Homework Equations The Attempt at a Solution Well, the reverse can also be done (making t to u). However, I don't know how to...

the question is ∫dx/ x^2*√(x^2-1) I use x=a sec ∅ x^2*√(x^2-1)= sec^2∅tan∅ x=sec ∅ dx= sec∅tan∅d∅ so it will become something like this ∫sec∅tan∅d∅/sec^2∅tan∅= ∫1/sec∅d∅=∫cos∅d∅ =sin∅+c But how can i change this sin in...

∫(cot^4 x) (csc^4 x) dx Wolfram wants to use the reduction formula, but I'm meant to do this just using identities and u substitution. I was thinking something along the lines of: =∫cot^4 x (cot^2 x + 1)^2 dx =∫cot^8 x + 2cot^6 x + cot^4 x dx but I don't know where to go from there.

Homework Statement You know the U substitution proofs for inverse trig functions that go like this: \int\frac{1}{a^{2}+x^{2}}dx \int\frac{a\frac{1}{a}}{a(1+\frac{x^2}{a^2})}dx let u = x/a du= dx/a ... \frac{1}{a}tan^{-1}(x/a)+cI have searched google and can't find any of these proofs for...

Homework Statement ∫3xdx/√(1-2x) Homework Equations The Attempt at a Solution so i tried making u=3x which makes du=3dx but that substitution doesn't get rid of the x unde the square root. i tried u=1-2x and that gives du=-2dx and that doesn't get rid of the x on top. So I'm...

Find ∫from .6 to 0 x^2/ sqrt(9-25x^2) dx My teacher worked this on the board a little confused O obviously the trig sub is asintheta. But it isn't in the right form yet. So get it there you pull out a 25 --) sqrt(25(9/25) - x^2 ) 5sqrt((9/25)-x^2 so x= (3/5) sintheta so dx = 3/5costheta. so...

The integral from 0 to pi/2 of: cos(t)/sqrt(1+sin^2(t)) dt I'm supposed to use trig. substitution to find the solution. I started by using the formula a^2+x^2 to get x=atanx. In this case, sin(t)=(1)tan(θ), and so cos(t)dt=sec^2(θ)dθ and so I substituted this into the equation and got...

Hi, I have the equation y' = y^2 + x^2 and am asked to linearise the equation with the appropriate substitution and then solve the resulting 2nd order linear equation. My issue is I am unsure what to substitute in for y. I can't seem to find a choice for y which the differential will be a...

Homework Statement [SIZE="4"]\int\frac{1}{\sqrt{16-x^2}}dx Homework Equations [SIZE="3"]csc\theta=\frac{4}{\sqrt{16-x^2}} [SIZE="3"]4cos\theta=x [SIZE="3"]-4sin\theta d\theta=dx [SIZE="3"]\theta=arccos(\frac{x}{4}) The Attempt at a Solution Using these facts, I concluded...

Homework Statement Given that n is a positive integer, prove ∫sin^n(x)dx=∫cos^n(x)dx from 0 -> pi/2 Homework Equations Perhaps sin^2(x)+cos^2(x)=1? Not sure. The Attempt at a Solution I honestly don't even know where to start. Should I set u=sin(x) or cos(x)? Doesn't seem to get...

Homework Statement ∫(4x^3)/√(x^2+4)dx Homework Equations The Attempt at a Solution So, I let x= 2tanθ dx= 2sec^2θ dθ So, √(4tan^2(θ)+4)=2secθ ∫(4x^3)/√(x^2+4)dx=∫((32tan^3(θ))/(2secθ))2sec^2(θ)dθ. Would it go to ∫16tan^3(θ)2sec(θ)dθ or ∫32tan^3(θ)sec(θ)dθ

When you have to integrate a function that requires substitution and you integrate it again, why is it wrong to keep the initial substitution? e.g. y''=2x/(1+x^2)^2 If you let u=1+x^2 then y'=-(1/u)+C. Why is it wrong to integrate that again with respect to u and then change back to x at...

Homework Statement Evaluate the following indefinite integral: ∫(sin(ln16x))/xdx Homework Equations The Attempt at a Solution let u = ln16x therefore du=16/16x=1/x ∫sinudu =-cosu =-cos(ln16x) Why is this showing as the wrong answer?

Homework Statement The definite integral of ∫(x^2 √(a^2-x^2) dx from 0 to a Homework Equations The Attempt at a Solution So i don't need actual help with this problem. I got the answer, (π*a^4)/16 and I verified with the back of the book. The question I have is whether this...

Homework Statement Use Part 2 of the Fundamental Theorem of Calculus to find the derivative. \int_3^x sin(t^{5}) \, dt Homework Equations The Attempt at a Solution I know the general idea of what I'm supposed to do as far as evaluate the indefinate integral and then do a subtraction of the...

θHomework Statement I'm trying to do an integration by substitution, but I'm completely stuck at the moment ∫(1-sin2θ)cosθ dθ Homework Equations ∫u dv = uv - ∫v du The Attempt at a Solution u = 1 - sin2θ dv = cosθ dθ du = -2sinθcosθ or -sin(2θ) v = sin I found du as...

I am trying to break a harmless ciphertext that uses a monoalphabetic substitution cipher. The ciphertext is exactly 244 characters long, without any spaces between words. It consists only of uppercase letters. ciphertext =...