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  • The value of the definite Integral ( sin x +cos x / 3 +sin2x ) [ where lower Limit 0 and upper limit pi/4]

The value of the definite Integral ( sin x +cos x / 3 +sin2x ) [ where lower Limit 0 and upper limit pi/4]

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Solution:    We have ,

                    int_0^fracpi4(fracsin x +cos x3+sin 2x)dx

               int_0^fracpi4(fracsin x +cos x3+sin 2x)dx =int_0^fracpi4fraccos x +sin x3+1-(sin x -cos x)^2dx

         Put          (sin x -cos x)=tRightarrow (cos x +sin x )dx=dt

   Rightarrow                   I=int _-1^0frac14-t^2dt=frac12 imes 2[ln (frac2+t2-t)]_-1^0 extrm=frac14[ln 1-ln 3^-1]=frac14ln 3.

Posted by

Deependra Verma

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