Discussion Forum



1)

 The area of the region bounded by x2 =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:

Option B

Explanation:

We have,

    x2=4y

    y=1

    y=4

1662021640_m1.PNG

 and the Y-axis lying  in the first quadrant.

$\therefore$ Required  area =  $\int_{1}^{4} \sqrt{4y}dy$

 =$2\left[\frac{2}{3}y^{3/2}\right]_{1}^{4}=\frac{4}{3}[4^{3/2}-1]$

$\frac{4}{3}(8-1)=\frac{4}{3}\times 7=\frac{28}{3}$