Question

The area of the region bounded by $x^2 = 4y, y = 1, y = 4$ and the y-axis lying in the first quadrant is ______ square units.

• A. $\frac{22}{3}$
• B. $\frac{28}{3}$
• C. 30
• D. $\frac{27}{4}$

Answer 1

Answer: (B)

We have,
$x^2 = 4y$
$y = 1$
$y = 4$

and the $Y$ -axis lying in the first quadrant.
$\therefore $ Required area $=\int\limits_{1}^{4} \sqrt{4 y} d y $
$=2\left[\frac{2}{3} y^{\frac{3}{2}}\right]_{1}^{4}=\frac{4}{3}\left[4^{\frac{3}{2}}-1\right] $
$=\frac{4}{3}(8-1)=\frac{4}{3} \times 7=\frac{28}{3}$