(sinx)^6+(sinx)^5在-2分之派到2 - 知识问答

(sinx)^6+(sinx)^5在-2分之派到2分之派的定积分?

3个回答

∫(- π/2→π/2) [sin⁶x + sin⁵x] dx
= ∫(- π/2→π/2) sin⁶x dx + ∫(- π/2→π/2) sin⁵x dx
前面偶函数,后面奇函数
= 2∫(0→π/2) sin⁶x dx + 0
= 2 * 5!/6! * π/2
= 2 * (5 * 3 * 1)/(6 * 4 * 2) * π/2
= 5π/16

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