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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2020

MathematicsMediumsingle choice

The area of the region (in sq. units), enclosed by the circle $x^{2} + y^{2} = 2$ which is not common to the region bounded by the parabola $y^{2} = x$ and the straight line $y = x$ , is

Question diagram: The area of the region (in sq. units), enclosed by the circl

Options:

Answer:

D

Solution:

Required area

$= 2 π - \int_{0}^{1} (\sqrt{x} - x) d x$

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

$= 2 π - (\frac{2}{3} - \frac{1}{2})$

$= 2 π - (\frac{1}{6})$

$= \frac{12 π - 1}{6} sq . units$

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

⏱ 2mℹ️ Source: PYQ_2020

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