∫(0->1) arcsinx.arccosx dx
=∫(0->1) arcsinx.[ π/2- arcsinx ] dx
=(π/2)∫(0->1) arcsinx dx -∫(0->1) (arcsinx)^2 dx
=(π/2) .(π/2 - 1) -[(π/2)^2 -2]
=2-(π/2)
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∫(0->1) arcsinx dx
=[x.arcsinx]|(0->1) -∫(0->1) x/√(1-x^2) dx
=π/2 + [ √(1-x^2) ]|(0->1)
=π/2 - 1
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∫(0->1) (arcsinx)^2 dx
= [x.(arcsinx)^2]|(0->1) -2∫(0->1)x.(arcsinx)/√(1-x^2) dx
=(π/2)^2 + 2∫(0->1) (arcsinx)d√(1-x^2)
=(π/2)^2 + 2[(arcsinx).√(1-x^2) ]|(0->1) -2∫(0->1) dx
=(π/2)^2 -2∫(0->1) dx
=(π/2)^2 -2