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

Engineering

Mathematics

Introduction to Area

Question

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

4/3

16/3

8/3

7/2

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Given curves are

$y = x^{2} - 1$

and

$y = 1 - x^{2}$

so intersection point are

$(\pm 1, 0)$

bounded area

$= 4 \int_{0}^{1} (1 - x^{2}) d x = 4 {[x - \frac{x^{3}}{3}]}_{0}^{1} = 4 (1 - \frac{1}{3}) \frac{8}{3} sq \cdot units$