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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesEasy2 minPYQ_2014

MathematicsEasysingle choice

The area in the first quadrant between $x^{2} + y^{2} = π^{2}$ and $y = sin x$ is

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Answer:

Solution:

$x^{2} + y^{2} = π^{2}$ is a circle of radius $π$ and centre at origin.
Required area $= Area of circle(1st quadrant) - \int_{0}^{π} sin x d x = \frac{π \cdot π ^{2}}{4} - [- cos x]_{0}^{π} = \frac{π ^{3}}{4} + (cos π - cos 0) = \frac{π ^{3}}{4} + (- 1 - 1) = \frac{π ^{3}}{4} - 2 = \frac{π ^{3} - 8}{4}$

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

⏱ 2mℹ️ Source: PYQ_2014

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