Homework Help: Integration cos theta help

1. Dec 15, 2008

kathrynag

1. The problem statement, all variables and given/known data

$$\int^{0}_{1}\frac{x^{2}}{\sqrt{1-x^{2}}}$$

2. Relevant equations

3. The attempt at a solution
Let x=sintheta
dx=cos theta
$$\int^{0}_{1}\sin^{2}$$
Now I get stuck

2. Dec 15, 2008

sutupidmath

well, i believe

$$sin^2x=\frac{1-cos2x}{2}$$ would help.

3. Dec 15, 2008

Staff: Mentor

You don't show dx in your original integral, but it should be there. You need to replace it and the square root in the denominator, using your substitution.

In your substitution, dx = cos(theta) d(theta).

4. Dec 15, 2008

Dick

There's a trig formula that let's you express sin(theta)^2 in terms of cos(2*theta). Can you find it?

5. Dec 15, 2008

kathrynag

so then i would make u=2x and du=2dx

6. Dec 15, 2008

sutupidmath

well first you woudl break it into 1/2-1/2 cos(2x) then if you want you can make that substituion, that would work.

7. Dec 15, 2008

kathrynag

Ok, well that's what I meant.

8. Dec 15, 2008