证明∫上面是a,下面是0,x^3f(x^2)dx=1/2∫上面为a^2,下面是0,xf(x)dx,(a大于0)其中 在讨论的区间连续.

令x²=t,则xdx=(1/2)dt,当x=0时,t=0；∵a>0,故当x=a时,t=a²
(0→a)∫x³f(x²)dx
=(0→a)∫x²f(x²)xdx
=(0→a²)∫tf(t)(1/2)dt
=(0→a²)(1/2)∫tf(t)dt
=(0→a²)(1/2)∫xf(x)dx