大学数学微积分试题

答:

1)

(0→π/2) ∫ sinx(cosx)^5 dx

=(0→π/2) - ∫ (cosx)^5 d(cosx)

=(0→π/2) -(1/6)*(cosx)^6

=0-(-1/6)

=1/6

2)

(0→π/2) ∫ xcosxdx

=(0→π/2) ∫ x d(sinx)

=(0→π/2) xsinx-∫ sinx dx

=(0→π/2) xsinx+cosx

=(π/2+0)-(0+1)

=π/2-1