1.

Evaluate: ∫sinx. sin(cosx)dx

Answer»

∫sinx. sin(cosx).dx 

Take cos x = t 

Diff w.r.t x, we have 

-sinx = dt/dx

-sin x.dx = dt 

sin x.dx = -dt 

⇒ ∫sin(cosx).sinx.dx 

= ∫sin(t)λ - dt = - ∫ sin t.dt 

= -x – cos t. + c =cost + c = cos(cosx) + c



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