Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2024

MathematicsMediumsingle choice

The area of the region bounded by the curves $x$ $= y^{2} - 2$ and $x = y$ is

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Solution:

Given, $x = y^{2} - 2$ and $x = y$ .On solving, $x = y^{2} - 2$ and $x = y$ , we get $(- 1, - 1)$ and $(2, 2)$ . Area of the shaded region, $A = \int_{- 1}^{2} y d y - \int_{- 1}^{2} (y^{2} - 2) d y = [\frac{y ^{2}}{2} - \frac{y ^{3}}{3} + 2 y]_{- 1}^{2} = (\frac{4}{2} - \frac{8}{3} + 4) - (\frac{1}{2} + \frac{1}{3} - 2) = \frac{10}{3} + \frac{7}{6} = \frac{27}{6} = \frac{9}{2} .$

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

⏱ 2mℹ️ Source: PYQ_2024

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