Question

x^2乘根号下1-x^2的定积分，上下限是1和0 求解答

Answer 1

令t=根号下1-x^2(t>=0),则 x^=1-t^2。0<=x<=1则0<=t<=1
原式=（1-t^2）t=t-t^3
接着就很简单了
答案1/4

Answer 2

令x=sina(-pai/2<a<pai/2)

=∫x^2√(1-x^2)dx

=∫sina^2cosadx

=∫sina^2dsina

=1/3sina^3
=1/3x^3
带值
=1/3