13. 2Sin 7

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Solution

The function is given as,

y = ∫ −π 2 π 2 sin 7 x dx

We have to calculate the integral of y.

Consider g( x )= sin 7 x.

g( x )= sin 7 x g( −x )= sin 7 ( −x ) g( −x )= ( sinx ) 7 ( −1 ) 7 g( −x )=− sin 7 x

It can be observed that g( x )=g( −x ). So, sin 7 x is an odd function.

Use property of odd functions ∫ −b b g( x )dx =0 if g( −x )=−g( x ) or g( x ) to solve integral.

y= ∫ −π 2 π 2 sin 7 x dx =0

Thus, the value of integral is 0.

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