MCQ
He area bounded by $y = x^2, x = y^{2 }$ is:
- ✓$1$
- B$\frac{1}{6}$
- C$\frac{3}{4}$
- D$\text{None}\text{ of}\text{ these}$
✓
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
$=\int\limits^1_0\sqrt{\text{x}}-\text{x}^2\text{dx}$
$=\frac{1}{2}\text{x}^\frac{3}{2}+\frac{\text{x}^3}{3}\Big|^1_0$
$=\frac{2}{3}+\frac{1}{3}$
$=1$
$\Rightarrow\text{y}=\sqrt{\text{x}}$
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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