Trig Substitution for Solving Integrals: Step-by-Step Guide

[yaho8888]

\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

<br /> \int \frac{9-9 \cos{\phi}}{3 \cos{\phi}} <br />

then what should I do?

 

[fikus]

Your sub was not correct. When you put in x=3sin(\Phi) you should also write what d\Phi cos now you are integrating over phi and not x anymore. Derivate your sub x=3sin(\Phi) and see what you get. You'll get an integral with cos^2(\phi). To solve that you shoud see the trig equation for cos(2x) and then it's easy.

hope it helps

 

[yaho8888]

I got to 9 \int \sin^2 \phi
now what?

 

[rock.freak667]

use cos2x=1-2sin^2x

 

[yaho8888]

9 \int \frac{1 + \cos{2x}}{2} dx

then what

 

[rock.freak667]

9 \int \frac{1 + \cos{2x}}{2} dx

then what

9\int (\frac{1}{2} + \frac{cos2x}{2} ) dx

Have you ever done Differentiation/Integration of trig functions?

 

[yaho8888]

9\int (\frac{1}{2} + \frac{cos2x}{2} ) dx

Have you ever done Differentiation/Integration of trig functions?

Sure I have. Ok thanks for help I got the whole problem cracked!