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f(t) = ∫<0, t> sinxdx - (sint/t^2)∫<0, t>x^2dx + ∫<t, π/2>sinxdx - sint∫<t, π/2>dx
= ∫<0, π/2>sinxdx - (sint/t^2)∫<0, t>x^2dx - (π/2-t)sint
f'(t) = 0 - [(tcost-2sint)/t^3]∫<0, t>x^2dx - sint + sint - (π/2-t)cost
= - (π/2-t)cost - [(tcost-2sint)/t^3]∫<0, t>x^2dx
= ∫<0, π/2>sinxdx - (sint/t^2)∫<0, t>x^2dx - (π/2-t)sint
f'(t) = 0 - [(tcost-2sint)/t^3]∫<0, t>x^2dx - sint + sint - (π/2-t)cost
= - (π/2-t)cost - [(tcost-2sint)/t^3]∫<0, t>x^2dx
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