求定积分!请给出具体步骤!∫(π/2,0) (cosx)^2*(sinx)^3dx

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求定积分!请给出具体步骤!∫(π/2,0) (cosx)^2*(sinx)^3dx
求定积分!请给出具体步骤!∫(π/2,0) (cosx)^2*(sinx)^3dx

求定积分!请给出具体步骤!∫(π/2,0) (cosx)^2*(sinx)^3dx
∫(π/2,0)(cosx)^2*(sinx)^3dx
=-∫(π/2,0)(cosx)^2*(sinx)^2d(cosx)
=∫(π/2,0)(cosx)^2*[(cosx)^2-1]d(cosx)
=∫(π/2,0)[(cosx)^4-(cosx)^2]d(cosx)
=(π/2,0)[(1/5)(cosx)^5-(1/3)(cosx)^3
=0-(1/5-1/3)
=2/15

∫(cosx)^2*(sinx)^3dx
=-∫ (cosx)^2*(sinx)^2dcosx
=-∫ (cosx)^2*[1-(cosx)^2]dcosx
=- (cosx)^3 / 3 + (cosx)^5 / 5+c
∫(π/2,0) (cosx)^2*(sinx)^3dx
=(-1/3+1/5 )-0
=-2/15

∫(cosx)^2*(sinx)^3dx
=-∫ (cosx)^2*(sinx)^2dcosx
=-∫ (cosx)^2*[1-(cosx)^2]dcosx
=- (cosx)^3 / 3 + (cosx)^5 / 5+c|(π/2,0)
=-(-1/3+1/5 )
=2/15