can someone help me find the antiderivative of:
f(x)=4x times the squareroot of (1-x^2)
f(x)=4x sqrt(1-x²)
use substitution
u=1-x^2
du=-2xdx
∫f(x)dx
=∫(4xsqrt(u))du/(-2x)
=-∫2sqrt(u)du
=-(4/3)u^(3/2)+C
=-(4/3)sqrt(1-x^2)^(3/2)+C
f(x)=4x times the squareroot of (1-x^2)
use substitution
u=1-x^2
du=-2xdx
∫f(x)dx
=∫(4xsqrt(u))du/(-2x)
=-∫2sqrt(u)du
=-(4/3)u^(3/2)+C
=-(4/3)sqrt(1-x^2)^(3/2)+C