Find-the-area-bounded-by-the-graph-y-x-2-and-y-2-x-2-for-0-x-2-

Question Number 173599 by Mastermind last updated on 14/Jul/22

Find the area bounded by the graph

y = x^{2} and y = 2 - x^{2} for 0 ⩽ x ⩽ 2 .

Commented by kaivan.ahmadi last updated on 14/Jul/22

x^{2} = 2 - x^{2} \Rightarrow x = \pm 1

\int_{0}^{1} (2 - x^{2} - x^{2}) d x = (- \frac{2}{3} x^{3} + 2 x) ∣_{0}^{1} =

(- \frac{2}{3} + 2) - (0) = \frac{4}{3}