定积分s(π/2,0)cos^3xdx

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定积分s(π/2,0)cos^3xdx定积分s(π/2,0)cos^3xdx定积分s(π/2,0)cos^3xdx∫(0π/2)cos³xdx=∫(0π/2)cosxcos²xdx

定积分s(π/2,0)cos^3xdx
定积分s(π/2,0)cos^3xdx

定积分s(π/2,0)cos^3xdx
∫(0 π/2) cos³x dx
=∫(0 π/2)cosxcos²x dx
=∫(0 π/2)(1-sin²x) d(sinx)
=sinx -sin³x/3 (0 π/2)
=(1 -1/3)-(0-0)
=2/3

∫[0,π/2] cos^3xdx
=∫[0,π/2] (1-sin^2x)dsinx
=(sinx-sin^3x/3)[0,π/2]
=2/3