∫(0→π/2) [(sint)^4－(sint)^6] dt
问题描述：
∫(0→π/2) [(sint)^4－(sint)^6] dt
答
这里用一个公式会简单些：∫ [0--->π/2] f(sinx)dx=∫ [0--->π/2] f(cosx)dx∫[0→π/2] (sin⁴t－sin⁶t) dt=∫[0→π/2] sin⁴t(1－sin²t) dt=∫[0→π/2] sin⁴tcos²t dt=1/2( ...