大一高数~计算定积分

2025-04-25 05:35:47
推荐回答(1个)
回答1:

第一个:x^3/(1+sin^2x)为奇函数,区间为对称区间,所以积分为0
只需要考虑∫cosx/(1+sin^2x)dx
=∫dsinx/(1+sin^2x)
=arctan(sinx)(-π/2,π/2)
=2arctan(sinπ/2)

=2arctan1
=2×π/2
=π