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 $=\underset{1}{\overset{4}{\int }}\sqrt{4y}dy$
$=2{\left[\frac{2}{3}{y}^{\frac{3}{2}}\right]}_1^4=\frac{4}{3}\left[4^{\frac{3}{2}}-1\right]$
$=\frac{4}{3}(8-1)=\frac{4}{3}\times 7=\frac{28}{3}$