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Question

(sin2xcos2x)dx=1(k)sin(2xa)+b. Find the value of k.

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Solution

Let I=(sin2xcos2x)dx
=2(1(2)sin2x1(2)cos2x)dx
=2.cos(2x+π4)dx=2.12sin(2x+π4)+c
=1(2)sin(π+2x+π4)+b (sin(π+θ)=sinθ)
=1(2)sin(2x(5π4))+b
Therefore a=5π4,k=2,b is any constant

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