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Question

If the integral of the function sin(80x)sin78x is sinaxsinbxc+D, where a,b,cR and D is the constant of integration, then the value of a+b+c is equal to

A
79
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B
81
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C
237
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D
240
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Solution

The correct option is C 237
I=sin(80x)sin78x dx
=sin(79x+x)sin78x dx
=(sin(79x)cosx+sin(x)cos79x)sin78x dx
=(sin(79x)sin78xcosx+sin79xcos79x)dx

Integrating by parts, we get
I=sin(79x)sin79x797979cos(79x)sin79x dx+cos(79x)sin79x dx
=sin(79x)sin79x79+D
a+b+c=237

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