sinx的平方和四次方在0到π/2的积分分别怎么算啊？谢谢了啊
热心网友
1.I=∫{0-π/2}sinx^2dx=∫{0-π/2}cosu^2du,(u=π/2=x)==2I=∫{0-π/2}sinx^2dx+∫{0-π/2}cosu^2du==∫{0-π/2}[sinx^2+cosx^2]dx=π/2==I=π/42.J=∫{0-π/2}sinx^4dx=∫{0-π/2}cosu^4du,(u=π/2=x)==π/2=∫{0-π/2}[sinx^2+cosx^2]^2dx=2J+2∫{0-π/2}sinx^2cosx^2dx==2J+[1/2]∫{0-π/2}sin2x^2dx=2J+[1/4]∫{0-π}sinx^2dx和1。同理]∫{0-π}sinx^2dx=π/2==》J=[1/2][π/2-π/8]=3π/16