The value of definite integral | sinx-cosx| , where lower limit =0 & upper limit =pi/2

Answers (1)

Solution : We have ,

               I=int_0^pi/2left | sin x-cos x 
ight |dx

      \Rightarrow I=int _0^pi/2sqrt2left | sin xcdot cos fracpi4-cos xcdot sinfracpi4 
ight |dx

    \Rightarrow I= int_0^pi/2sqrt2left | sin(x-pi/4) 
ight |dx

         Put ,    x-pi/4=tRightarrow dx=dt

     I=int_frac-pi4^fracpi4sqrt2left | sin t 
ight |dt=2(sqrt2-1)

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