Substitution method Definition and 23 Threads

I'm really stuck on this one, I was able to get the answer but not by the substitution method. So its the weight as A and B so I get A + B = 24 A(3) = B(5) so in my head I calculate a few pairs, 3 x 5 = 15 but 3 + 5 only = 8 so the next pair would be 10 and 6 which is still to small so I move...

What I have done: I changed all fractions to common denom and that gave me 5y-5x=1 (1) *I numbered the fractions 5y+2x=5 (2) Then: 5y=5-2x Substitute into equation 1 (5-2x)-5x=1 5-7x=1 x=4/7 Thing is my answer says I should be getting x=0 Any hints?

Homework Statement Question: To solve the integral ##\int \frac{1}{\sqrt{x^2-4}} \,dx## on an interval ##I=(2,+\infty)##, can we use the substitution ##x=\operatorname {arcsint}##? Explain Homework Equations 3. The Attempt at a Solution [/B] This is my reasoning, the function ##\operatorname...

Look, I was wondering if substituting the variable more than once is valid and hence the definite integral intervals change this way. Consider the following integral (I'm working for finding the volume of a solid of revolution): *\pi \int_{-3}^{5}3^{2}-(\sqrt{\frac{y+3}{2}}+1)^2dy Personally I...

Homework Statement Evaluate the following integral using a change of variables: \int\frac{dx}{\sqrt{1-\sin^4{x}}} Homework Equations If f(x)=g(u(x))u'(x) and \int g(x)dx = G(x) +C then \int f(x)dx = G(u(x))+C The Attempt at a Solution It seems helpful to first simplify a little to obtain...

Homework Statement So it says solve this wave equation : [y][/tt] - 4 [y][/xx] = 0 on the domain -infinity<x<infinity with initial conditions y(x,0) = e^(-x^2), yt(x,0) = x*(e^(-x^2)) Homework Equations I used the D Alembert's solution which is 1/2(f(x+ct)+f(x-ct)) + 1/2c ∫ g(z) dz The...

It is common that we replace \int u(x)v'(x)dx by \int udv where both u and v are continuous functions of x. My question is, must we ensure that u can be written as a function of v before applying this? The above substitution method is involved in the proof of integration by parts but I cannot...

Hello! I need help to integrate the square root of: p x2 + x4 by the method of substitution, p is just a constant. I've been trying for a long time but I can't get it right. I know the answer and it still doesn't help. Thanks! (sorry, I don't know the Latex stuff)

Hello all I am working on this integral \[\int \frac{x^{2}+1}{x^{4}+1}dx\]Now, I have tried this way: \[u=x^{2}+1\] after I did: \[\int \frac{x^{2}+1}{\left ( x^{2}+1 \right )\left ( x^{2}-1 \right )}dx\] But I got stuck, I got: \[\frac{1}{2}\cdot \int \frac{1}{u\sqrt{u-1}}dx\] I thought...

Hello I need to solve \[\int \sqrt{x^{3}+4}\cdot x^{5}dx\] using the substitution method. I did \[u=x^{3}+4\] but I got stuck with it. thanks!

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...

Say we are solving an indefinite integral ∫x√(2x+1) dx. According to the textbook, the solution goes like this. Let u = 2x+1. Then x = (u-1)/2. Since √(2x+1) dx = (1/2)√u du, x√(2x+1) dx = [(u-1)/2] * (1/2)√u du. ∫x√(2x+1) dx = ∫[(u-1)/2] * (1/2)√u du. <= What justifies this?? The...

I feel as if I have made the correct substitution, what am I missing? See Attachment. Thanks, Dane

Substitution method with Integration by Parts? Homework Statement Evaluate the integral... ∫x^3[e^(-x^2)]dx Homework Equations ∫udv=uv-∫vdu The Attempt at a Solution I first tried using integration by parts setting u and dv equal to anything and everything. This seemed to make...

use the subtitution method to solve. x^2 + 2y = 9 x - y + 3 = 0 y=x+3 -> (3) substitute for y with x+3, you get: x^2+2(x+3)=9 x2+2x−3=0 factorize it to get: (x+3)(x−1)=0 x=−3,x=1 substitute for each value of x in equation 3 x=−3y=−3+3=0 x=1y=1+3=4...

Homework Statement y'=y+y^3 Homework Equations The Attempt at a Solution I set y=v, dy/dx = dv/dx. Substituted back into original equation ST dv/dx = v + v^3. Cross multiply, then divide yielded dv/(v+v^3) = dx. After that, I have no clue. The book gives the following...

Homework Statement Hi there. I'm dealing with undefined integrals now. And I found this one that I don't know how to solve. The problem statement says: Solve the next integrals using the substitution method. \displaystyle\int_{}^{}\displaystyle\frac{\cos(x)}{\sin^3(x)}The Attempt at a Solution...

Hi everyone, Can you tell me how to integrate the following equation? \int\frac{1}{x^2 + 1} \ dx I've tried the substitution method, u = x^2 + 1, du/dx = 2x. But the x variable is still exist. Also, the trigonometry substitution method, but the denominator is not in \sqrt{x^2 + 1}...

\begin{array}{l} \frac{{dy}}{{dx}} = \frac{{4x^2 + 5xy + y^2 }}{{x^2 }} \\ \\ \frac{{dy}}{{dx}} = 4 + \frac{{5y}}{x} + \left( {\frac{y}{x}} \right)^2 \\ \\ {\rm{Let }}v = y/x\,\,\,\, \Rightarrow \,\,\,\,y = vx \\ \\ \frac{{dy}}{{dx}} = 4 + \frac{{5v}}{{xx}} + \left(...

Homework Statement \left( {x + y} \right)y' = x - y Homework Equations Back of book: x^2 - 2xy - y^2 = C The Attempt at a Solution I'm not sure how to start this problem. In the examples in the book, they make a substitution, v=something, and all that was left were v's and...

Homework Statement dy/dx = \frac{[2cos(x)^2-sin(x)^2+y^2]}{[2cos(x)]} Substitute y(x) = sin(x) + \frac{1}{u(x)} Homework Equations By doing the substitution, it will yield the differential equation for u(x) du/dx = -u tan(x) - \frac{1}{2}sec(x) The Attempt at a Solution I figured out i...

Evaluate the following integral using integration by substitution: http://img254.imageshack.us/img254/750/44900023cm4.png [/URL] Here is my attempt: Let x = sinu, then dx/du = cosu Substituting gives, ∫1/(1-sin2u)×cosu du = ∫1/(1-sin2u)×cosu du = ∫cosu/√cos2u du = ∫cosu/cosu...

Hi, I have another problem about substitution Method. I think this method is used to make the problem to solve in easy way but it is making my procedure too long for this problem. Can you solve it by substitution method. S (x+5)½/x-4 dx where S is the sign of integral. The answer of...