设 t = x/2，则 dx = 2*dt，当 x = π 时，t = π/2。则积分限变为 [0, π/2]
∫[sin(x/2)]^3 *dx
=∫[sint]^3 * 2*dt
=2*∫(sint)^2 * sint *dt
=2*∫[1 - (cost)^2] * sint *dt
=2*∫sint *dt - 2∫(cost)^2 * sint *dt
=-2cost - 2*∫(cost)^2 * d(-cost)
=-2*[cos(π/2) - cos0] + 2*∫(cost)^2 *d(cost)
=-2*[0 -1] +2/3* (cost)^3
=2 + 2/3*{[cos(π/2)]^3 -(cos0)^3]
=2 + 2/3 * [0 - 1]
=2 - 2/3
=4/3
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