Question

求定积分∫(上限π/2,下限-π/2)sinsinxdx

Answer 1

f(x) = sin(sinx)
f(-x) = sin[sin(-x)]
= sin(-sinx)
= -sin(sinx)
= -f(x)
f(x)是奇函数,所以由定积分定理得∫(-π/2,π/2)sin(sinx)dx = 0