求定积分∫（（1-x^2）^3）^0.5dx 积分区间为0到1
问题描述：
求定积分∫（（1-x^2）^3）^0.5dx 积分区间为0到1
答
令x = sinz,dx = cosz dz
∫(0→1) (1 - x²)^(3/2) dx
= ∫(0→π/2) cos³z * (cosz dz)
= ∫(0→π/2) cos⁴z dz
= (4 - 1)!/4!* π/2
= 3!/4!* π/2
= (3 * 1)/(4 * 2 * 1) * π/2
= 3π/16