Question

高等数学，微积分问题求解，谢谢！

Answer 1

原式=∫(0,T/4)(1-cos2wt)/2 dt
=1/2 t|(0,T/4) -∫(0,T/4)(cos2wt)/2 dt
=T/8 -1/2 ×1/(2w) ∫(0,T/4)(cos2wt) d2wt
=T/8 -1/(4w) sin2wt |(0,T/4)
=T/8-1/(4w) (sin(wT/2)-0)
又T=2π/w
代入，得
原式=π/(4w) -1/(4w) (sin(π)-0)
=π/(4w)-0
=π/(4w)

Answer 2

∫(0,T/4)sin²wtdt
=1/2w*∫(0,T/4)(1-cos2wt)/2 d2wt
=1/2w*(2wt-sin2wt)/2 (0,T/4)
=t/2-sin2wt/4w (0,π/2w)
=π/4w

Answer 3

t Sin[欧米伽t]^2=1/2 π Sin[欧米伽t]^2