题目是利用对称区间上的函数的奇偶性求定积分

因为f(x)=(sinx)^4=(-sinx)^4=f(-x)
所以f(x)是偶函数
π/2 π/2
∫ ()dx
-π/2 0
2∫4(sinx)^4 xdx=8∫(sinx)^4 xdx
(sinx)^4
= (sinx^2)^2
= ((1 - cos2x)/2)^2
= (1 - 2cos2x + (cos2x)^2)/4
= 0.25 - 0.5cos2x + 0.125(1 + cos4x)
= (cos4x)/8 - (cos2x)/2 + 3/8
8∫ (sinx)^4dx
= 8∫ ((cos4x)/8 - (cos2x)/2 + 3/8)dx
= 8∫ ((cos4x)/8)dx - 8∫ ((cos2x)/2)dx + 8∫ (3/8)dx
= (1/4)∫ cos4xd4x - 2∫ cos2xd2x + 3x
= (sin4x)/4 - 2sin2x + 3x + C
f(π/2)-f（0）=3/2π