The area bounded by y = x^2 and y = 1 - x^2 is: - Vidyadip

MCQ

The area bounded by $y = x^2$ and $y = 1 - x^2$ is:

✓
$\frac{\sqrt{8}}{3}$
B
$\frac{16}{3}$
C
$\frac{32}{3}$
D
$\frac{17}{3}$

✓

Answer

Correct option: A.

$\frac{\sqrt{8}}{3}$

Required are
$=2\Bigg[\int\limits^\frac{1}{\sqrt{2}}_0(1+\text{x}^2)\text{dx}-\int\limits^\frac{1}{\sqrt{2}}_0\text{x}^2\text{dx}\Bigg]$
$=2\Bigg[\text{x}+\frac{\text{x}^3}{3}\Bigg]^\frac{1}{\sqrt{2}}_0-2\Bigg[\frac{\text{x}^3}{3}\Bigg]^\frac{1}{\sqrt{2}}_0$
$=\frac{\sqrt{8}}{3}$

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