The value of the integral \int_{0}^{\pi} \int_{y}^{\pi} \frac{\sin x}{x} d x d y, is equal to

GATE Electronics and Communications (EC) 2019 Solved Paper

Question : 18 of 65

Marks: +1, -0

The value of the integral

∫↙{0}↖{π} ∫↙{y}↖{π} \;{\sin x}/{x} d x d y

, is equal to

Solution:

By changing order of integration

∫↙{x=0}↖{x=π}(∫↙{y=0}↖{y=x} d y) \;{\sin x}/{x} d x

∴ ∫↙{x=0}↖{π} x \;{\sin x}/{x} d x

∴ ∫↙{x=0}↖{π} x \sin x d x

∴ [-\cos x]_{0}^{π}=2

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