三角函数在0到2π的积分
∫(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,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。