定积分上π/2下0,x²cosxdx

定积分上π/2下0,x²cosxdx
定积分上π/2下0,x²cosxdx

定积分上π/2下0,x²cosxdx
∫(0→π/2) x²cosx dx
= ∫(0→π/2) x² dsinx
= [x²sinx]：(0→π/2) - ∫(0→π/2) 2xsinx dx
= π²/4 - (- 2)∫(0→π/2) x dcosx
= π²/4 + 2[xcosx]：(0→π/2) - 2∫(0→π/2) cosx dx
= π²/4 + 0 - 2[sinx]：(0→π/2)
= π²/4 - 2
= (π² - 8)/4