MCQ
Area between the curves $y = x^3$ and $y = \sqrt x$ is
- A$\frac{5}{3}$
- B$\frac{5}{4}$
- ✓$\frac{5}{12}$
- DNone
✓
Answer
Correct option: C.
$\frac{5}{12}$
c
The curve $y=\sqrt{x}$ is $y^{2}=x ;(y \geq 0) \quad \ldots$ $(i)$
The curve $y=\sqrt{x}$ is $y^{2}=x ;(y \geq 0) \quad \ldots$ $(i)$
and $y=x^{3}$ .....$(ii)$
Point of intersection are $(0,0) \&(1,1)$
$\therefore $ Required area $ = \int\limits_0^1 {\left( {{{\rm{y}}_2} - {{\rm{y}}_1}} \right)dx} $
$ = \int\limits_0^1 {\left( {\sqrt x - {x^3}} \right)dx} $
${=\frac{5}{12}}$
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