Q.

The value of the integral  ∫0π|sin2x|dxis  _____

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answer is 2.

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Detailed Solution

∫0πsin2xdx=12∫02πsintdt=12×2∫0πsint  dt=2               (    put x=t2 )                ( since  ∫02af(x)dx =2 ∫0af(x)dx    if f (2a-x)= f(x)                                          here           sin (2π-x)=sinx   )
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The value of the integral  ∫0π|sin2x|dxis  _____