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Question

Integrate the following function with respect to x
1sinxcosx

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Solution

Marks1 2 3 4 5 6 7 8 9
Frequency 1 2 1 3 5 4 2 1 1
1sinxcosx×sinx+cosxsinx+cosx
sinx+cosxsin2xcos2xsinx+cosx2sin2x1
sinx+cosx12sin2x
(1) sinxcos2xdx=122(ln/2sinx+2ln/2sinx2)
122 ln|2sinx+2|lnI2sinx2I
Thus
1sinxcosxdx=cosxsinxcos2xdx=sinxcos3x+cosxcos3xdx


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