sin x7.sin (x -a)

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Solution

The given function is,

f( x )= sinx sin( x−a ) = sin( x−a+a ) sin( x−a ) .

Integrate both sides,

∫ f( x )dx = ∫ sin( x−a )cosa+cos( x−a )sina sin( x−a ) dx = ∫ sin( x−a )cosa sin( x−a ) dx + ∫ cos( x−a )sina sin( x−a ) dx =cosa ∫ dx +sina ∫ cot( x−a )dx =xcosa+sinalog| sin( x−a ) |+c

Thus, integration of f( x ) is xcosa+sinalog| sin( x−a ) |+c.

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