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

$$\int \frac{9-9 \cos{\phi}}{3 \cos{\phi}}$$

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!