Find area bounded by curves (x,y):y ^2 andy=x : - Vidyadip

MCQ

Find area bounded by curves $\{(\text{x},\text{y}):\text{y}\geq\text{x}^2\text{ andy}=\text{x}\}$ :

A
$\frac{5}{3}$
B
$\frac{1}{2}$
✓
$\frac{1}{3}$
D
$\frac{1}{9}$

✓

Answer

Correct option: C.

$\frac{1}{3}$

$=\text{y}=\text{x}=\{\text{x};\text{x}\geq0-\text{x};\text{x}<0\}<0\}\text{p}$ and $Q$ are$x^2 = x$
$= x2 - x = 0 x(x - 1) = 0 x = 0,1Q =1$ similarlyp
$=-\text{A}=\int\limits^1_0\text{x}-\text{x}^2\text{ dx}$
$=\text{A}=\Big[\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}\Big]^1_0$
$\text{A}=\frac{1}{2}-\frac{1}{3}$
$=\text{A}=\frac{1}{3}$

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