MCQ
Area bounded by curves $y = {x^2}$ and $y = 2 - {x^2}$ is
- ✓$8/3$
- B$3/8$
- C$3/2$
- DNone of these
✓
Answer
Correct option: A.
$8/3$
a
(a) $y = {x^2}$.....$(i)$
(a) $y = {x^2}$.....$(i)$
$y = 2 - {x^2}$.....$(ii)$
$\therefore $ By equation $(i)$ and $(ii),$ we get, $x = \pm 1$
$\therefore $ $y = \pm 1$
$\therefore $ Required area $ = 2\left[ {\int_0^1 {(2 - {x^2})dx - \int_0^1 {{x^2}dx} } } \right]$
$ = 2\,\left[ {2x - \frac{{2{x^3}}}{3}} \right]_0^1 = 4\left[ {x - \frac{{{x^3}}}{3}} \right]_0^1 = 4\left( {\frac{2}{3}} \right) = \frac{8}{3}$.
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