Evaluate the following integral:

Let us assume .....….equation 1


By property, we know that


thus


.....………….equation 2


Since


Adding equation 1 and equation 2



We know



Thus





Adding and subtracting 1



)


We know



)


Let


Let


.......equation 3


Solving I1:




We know b and a being the upper and lower limits respectively.




Solving I2:



Using trigonometric identity and formula




Taking common





Let


Differentiating both sides, we get,




For x = 0




For x = π





Substituting the values


Thus





We know b and a being the upper and lower limits respectively




Substituting values in equation 3




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