一道高数题——定积分去绝对值

求问下一步怎么做,参考答案是-4/3
2025-05-21 02:08:09
推荐回答(1个)
回答1:

∫u^(1/2) du=(2/3)u^(3/2)+C
下一步呢
=(2/3)(sint)^(3/2) 【0到π/2】 -(2/3)(sint)^(3/2) 【π/2到π】
=(2/3)[(sinπ/2)^(3/2)-(sin0)^(3/2)]-(2/3)[(sinπ)^(3/2)-(sinπ/2)^(3/2)]
=(2/3)[1-0]-(2/3)[0-1]
=2/3+2/3=4/3
答案肯定是正的,正数函数积分的数值肯定是正的