The area (in sq. unit) of the region described by A = x , y : x 2 + y 2 ≤ 1 and y 2 ≤ 1 - x is

Area of shaded region = area of semicircle + area of region B C A = π 2 + 2 ∫ 0 1 1 - x · d x = π 2 + 2 - 2 3 1 - x 3 / 2 0 1 = π 2 - 4 3 - 1 = π 2 + 4 3 sq. unit

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2014

MathematicsMediumsingle choice

The area (in sq. unit) of the region described by $A = \{(x, y) : x^{2} + y^{2} \leq 1 and y^{2} \leq 1 - x\}$ is

Question diagram: The area (in sq. unit) of the region described by A = x , y

Options:

Answer:

Solution:

Area of shaded region $=$ area of semicircle $+$ area of region $B C A$

$= \frac{π}{2} + 2 \int_{0}^{1} \sqrt{1 - x} \cdot d x$

$= \frac{π}{2} + 2 (- \frac{2}{3}) {[{(1 - x)}^{3 / 2}]}_{0}^{1}$

$= \frac{π}{2} - \frac{4}{3} (- 1)$

$= \frac{π}{2} + \frac{4}{3}$ sq. unit

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2014

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