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Question

The value of the integral sin(60x)sin58x dx is
(where C is the constant of integration)

A
sin(59x)sin58x58+C
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B
sin(58x)sin59x60+C
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C
sin(60x)sin59x59+C
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D
sin(59x)sin59x59+C
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Solution

The correct option is D sin(59x)sin59x59+C
I=sin(60x)sin58x dx
=sin(59x+x)sin58x dx
=(sin(59x)cosx+cos(59x)sinx)sin58x dx
=[sin(59x)sin58xcosx+sin59xcos(59x)]dx

Integrate sin(59x)sin58xcosx by parts, we get

=sin(59x)sin59x59cos(59x)sin59x dx+cos(59x)sin59x dx
=sin(59x)sin59x59+C

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