Question

The area bounded by the parabola $y^2=x$ straight line $y=4$ and $y$ -axis is square units is

• A. $16/3sq.$ unit
• B. $64/3sq.$ unit
• C. $7\sqrt{2}sq.$ unit
• D. None of these

Answer 1

Answer: (B)

Line $y=4$ meets the parabola $y^2=x$ at $A$
$\therefore 16=x$ and $A$ is (16,4)

$\therefore$ Required area
$<br/>\begin{array}{l}<br/>={\int }_{y=0}^{4}xdy\\ <br/>={\int }_{y=0}^4{y}^{2}dy\\ <br/>={\left[y^3/3\right]}_0^4\\ <br/>=\frac{64}{3}\text{ sq units }<br/>\end{array}<br/>$