积分区间为【2,5】 求∫(x^2)cosxdx
问题描述：
积分区间为【2,5】 求∫(x^2)cosxdx
答
∫[2,5] (x^2)cosxdx
=∫[2,5] (x^2)dsinx
= x^2sinx |[2,5] -∫[2,5] sinxd(x^2)
= [25sin5-4sin2] -2∫[2,5] xsinxdx
= [25sin5-4sin2] + 2∫[2,5] xdcosx
= [25sin5-4sin2] + 2{xcosx|[2,5] - ∫[2,5] cosxdx }
= [25sin5-4sin2] + 2{ [5cos5-2cos2] - sinx|[2,5] }
= [25sin5-4sin2] + [10cos5-4cos2] - [2sinx5-2sin2]
= [23sin5-2sin2] + [10cos5-4cos2]