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
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