I can't seem to take the integral from 0 to 1 of x^3 sqrt(1-x^2)dx past sin^(theta) cos^2(theta) d(theta)

Question

I can't seem to take the integral from 0 to 1 of x^3 sqrt(1-x^2)dx past  sin^(theta) cos^2(theta) d(theta)

anonymous · Answer

$$\int\limits_{0}^{1}  x^3 \sqrt{1-x^2}dx$$

anonymous · Answer

I used x = sin (theta)   dx= cos (theta) d (theta)

anonymous · Answer

I have been working on calc for 9 hours straight and my brain is mush

anonymous · Answer

try substituting
u=1-x^2
du=-2x dx

anonymous · Answer

do u-sub. It's actually faster in this case

anonymous · Answer

thanks Ill try it we were working on trig substitutions so I was just stuck in that mindset

anonymous · Answer

you could do trig. But since the answer will come out the same, so why not pick the shortest way. You have plenty of examples to try trig sub