Question

设a=定积分0到2√4-x∧2dx，a为多少

Answer 1

Answer 2

a=∫(0->2)√(4-x^2) dx
let
x=2siny
dx=2cosy dy
x=0, y=0
x=2, y=π/2

∫(0->2)√(4-x^2) dx
=4∫(0->π/2) (cosy)^2 dy
=2∫(0->π/2) (1+cos2y) dy
=2[ y + (1/2)sin2y] |(0->π/2)
=π
=> a=π