设A=∫-π/2→π/2 f(x)*(sinx)^4 dx
令x=-t,得
∫π/2→-π/2 f(-t)*(sint)^4 【-dt】
=∫-π/2→π/2 f(-x)*(sinx)^4 dx
所以
2A=∫-π/2→π/2 f(x)*(sinx)^4 dx＋∫-π/2→π/2 f(-x)*(sinx)^4 dx
=∫-π/2→π/2 【 f(x)＋f（-x）】*(sinx)^4 dx
=∫-π/2→π/2 sin²x*(sinx)^4 dx
=2∫0→π/2 (sinx)^6 dx
=2×5/6×3/4×1/2×π/2
所以
A=5/6×3/4×1/2×π/2
=5π/32