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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minQB

MathematicsMediumsingle choice

If $c > 0$ and the area of the region enclosed by the parabolas $y = x^{2} - c^{2}$ and $y = c^{2} - x^{2}$ is 576, then $c =$

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Solution:

The parabolas meet at $x = \pm c$ . Area $= 4 \int_{0}^{c} (c^{2} - x^{2}) d x = 4 [c^{2} x - \frac{x ^{3}}{3}]_{0}^{c} = \frac{8 c ^{3}}{3} = 576$ , so $c^{3} = 216$ and $c = 6$ .

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

⏱ 2mℹ️ Source: QB

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