recall that sin(2x) = 2sinxcosx, so ...
π/2
∫ sin(x)cos(x) dx
π/6
π/2
= ∫ (1/2) sin (2x) dx
π/6
= [ - (1/4) cos(2x) ] from π/6 to π/2
take over , make sure you get 3/8 or .375
π/2
∫ sin(x)cos(x) dx
π/6
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