Area of the region in which point p ( x , y ) , { x > 0 } lies; such that y ≤ 16 − x 2 and tan − 1 ( x y ) ≤ 3 π is

The region is bounded by the rays y = ± 3 x ( x > 0 ) and the circle x 2 + y 2 = 16 (with x ≤ 4 ). Required area = area of △ O A Q + area of sector O A P = 2 1 × 4 × 4 3 + 6 π ( 4 × 4 ) = 3 8 π + 8 3 .

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minQB

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Area of the region in which point $p (x, y), {x > 0}$ lies; such that $y \leq 16 - x^{2}$ and $tan^{- 1} (\frac{y}{x}) \leq \frac{π}{3}$ is

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The region is bounded by the rays $y = \pm 3 x (x > 0)$ and the circle $x^{2} + y^{2} = 16$ (with $x \leq 4$ ). $\underline{Required area = area of △ O A Q + area of sector O A P = \frac{1}{2} \times 4 \times 43 + \frac{π ( 4 \times 4 )}{6} = \frac{8 π}{3} + 83 .}$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by Miscellaneous Curves

⏱ 2mℹ️ Source: QB

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