How do you find the antiderivative of int xsqrt(1-x^2) dx?
2 Answers
The answer is
Explanation:
We perform this by substitution
Let
Therefore,
Explanation:
Here's an alternative answer using trig substitution.
Let
=intsinthetasqrt(1 - sin^2theta) * costheta d theta
=intsintheta sqrt(cos^2theta) * costheta d theta
=int sintheta costhetacostheta d theta
=int sin thetacos^2theta d theta
Now make a substitution. Let
=int sin theta cos^2theta * (du)/(-sintheta)
=-int u^2du
=-1/3u^3 + C
=-1/3cos^3theta + C
We know from our initial substitution that
=-1/3(1 - x^2)^(3/2) + C
Hopefully this helps!