QJEEM20Ma0487: JEE Main 2020 Mathematics - Class 12 JEEM20Ma0487 Solution: The area (in sq. units) of the region enclosed by the curves y…

Question

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The area (in sq. units) of the region enclosed
by the curves y = x² – 1 and y = 1 – x² is equal to :

Accepted Answer

A =

\int_{- 1}^{1} ((1 - x^{2}) - (x^{2} - 1)) d x

=

\int_{- 1}^{1} (2 - 2 x^{2}) d x

=

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

=

4 {(x - \frac{x^{3}}{3})}_{0}^{1}

=

4 (\frac{2}{3})

=

\frac{8}{3}

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