Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2020

MathematicsMediumsingle choice

The area (in sq. units) of the region enclosed by the curves $y = x^{2} - 1$ and $y = 1 - x^{2}$ is equal to:

Answer:

Solution:

Given curves are

$y = x^{2} - 1$

and

$y = 1 - x^{2}$

so intersection point are $(\pm 1, 0)$

$∴$ bounded area

$= 4 \int_{0}^{1} (1 - x^{2}) d x$

$= 4 {[x - \frac{x^{3}}{3}]}_{0}^{1}$

$= 4 (1 - \frac{1}{3}) \frac{8}{3} sq \cdot units$

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

⏱ 2mℹ️ Source: PYQ_2020

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