Prove that the integral from 0 to 2 of sqrt(4-x^2)dx = pi

Question

Should I use a trip substitution for this?

Thanks for the help.

Answer 1

yes: 2sinθ = x
so, 4-x^2 = 4-4sin^2θ = 4cos^2 θ
and √(4-x^2) = 2cosθ

naturally, you could also say 2cosθ = x