求sin²x在0到π的定积分

求sin²x在0到π的定积分
求sin²x在0到π的定积分

求sin²x在0到π的定积分
∫(0,π)sin²xdx
=∫(0,π)[1-cos(2x)]/2 dx
=∫(0,π)[1-cos(2x)]/4 d(2x)
=(1/4)∫(0,π)[1-cos(2x)]d(2x)
=(1/4) [2x-sin(2x)/2] |(0,π)
=(1/4)[2π-sin(2π)/2-2×0-sin(0)/2]
=(1/4)(2π)
=π/2
提示：利用三角函数公式cos(2x)=1-2sin²x,再将d(x)换成(1/2)d(2x),剩下的就好办了.

∫(0到π) sin²xdx
=∫(0到π) (1-cos(2x))/2 dx
=0.5x-0.25sin(2x) | (上π下0)
=0.5π
=π/2