He area bounded by y=x^2, x=y^2 is: - Vidyadip

MCQ

He area bounded by $y=x^2, x=y^2$ is:

✓
$1$
B
$\frac{1}{6}$
C
$\frac{3}{4}$
D
None of these

✓

Answer

Correct option: A.

$1$

$=\text{y}=\text{x}^2,\text{y}^2=\text{x}$
$\Rightarrow\text{y}=\sqrt{\text{x}}$
The curves intersect at $(0, 0)$ and $(1,1)$ Area between the curves is given by
$=\int\limits^1_0\sqrt{\text{x}}-\text{x}^2\text{dx}$
$=\frac{1}{2}\text{x}^\frac{3}{2}+\frac{\text{x}^3}{3}\Big|^1_0$
$=\frac{2}{3}+\frac{1}{3}=1$

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