Area bounded by the curve $y = x + s i n x$ and its inverse function between the ordinates $x = 0$ and $x = 2 π$ is

π

sqp. units

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π

sq. units

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8 sq. units

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π

sq. units

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Solution

The correct option is B 8 sq. units
Inverse function is the mirror image with respect to $y = x$
Then area bounded by $x + sin x$ and its inverse function is $4 \int_{0}^{π} (x + sin x - x) d x = 8$

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