JEE MAIN - Mathematics (2020 - 7th January Morning Slot - No. 19)
The area of the region, enclosed by the circle x2 + y2 = 2 which is not common to the region bounded by the parabola y2 = x and the straight line y = x, is:
$${1 \over 6}\left( {24\pi - 1} \right)$$
$${1 \over 3}\left( {12\pi - 1} \right)$$
$${1 \over 3}\left( {6\pi - 1} \right)$$
$${1 \over 6}\left( {12\pi - 1} \right)$$
Explanation
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Required area = Area of circle – $$\int\limits_0^1 {\left( {\sqrt x - x} \right)dx} $$
= $$\pi $$r2 - $$\left( {{{2{x^{3/2}}} \over 3} - {{{x^2}} \over 2}} \right)_0^1$$
= $$\pi {\left( {\sqrt 2 } \right)^2}$$ - $${1 \over 6}$$
= $${1 \over 6}\left( {12\pi - 1} \right)$$
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