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f'(x) = xsinx
f(π/2)=0
∫(0->π/2) f(x) dx
=[xf(x)]|(0->π/2) -∫(0->π/2) xf'(x) dx
=-∫(0->π/2) x^2.sinx dx
=∫(0->π/2) x^2 dcosx
=[x^2.cosx]|(0->π/2) -2∫(0->π/2) xcosx dx
=-2∫(0->π/2) xdsinx
=-2[xsinx]|(0->π/2) +2∫(0->π/2) sinx dx
=-π -2[cosx]|(0->π/2)
=-π +2
f(π/2)=0
∫(0->π/2) f(x) dx
=[xf(x)]|(0->π/2) -∫(0->π/2) xf'(x) dx
=-∫(0->π/2) x^2.sinx dx
=∫(0->π/2) x^2 dcosx
=[x^2.cosx]|(0->π/2) -2∫(0->π/2) xcosx dx
=-2∫(0->π/2) xdsinx
=-2[xsinx]|(0->π/2) +2∫(0->π/2) sinx dx
=-π -2[cosx]|(0->π/2)
=-π +2
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