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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 71

The area (in sq. units) of the part of the circle x2+y2=36x^2+y^2=36, which is outside the parabola y2=9xy^2=9x, is :

Choose one option
Answer and worked solution

Official answer: B

Inside both. They meet at x=3x=3. Area =2[∫033x dx+∫3636−x2 dx]=2[63+6π−932]=12π+33=2\left[\int_0^33\sqrt x\,dx+\int_3^6\sqrt{36-x^2}\,dx\right]=2\left[6\sqrt3+6\pi-\frac{9\sqrt3}2\right]=12\pi+3\sqrt3.

Outside the parabola 36π−(12π+33)=24π−3336\pi-(12\pi+3\sqrt3)=24\pi-3\sqrt3.

(B)

Topics:Area between curves
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