Question

Area of the region bounded by the curve `y^2=4x`, y-axis and the line `y=3` is (A) `2` sq. units (B) `9/4` sq. units (C) `6sqrt(3)` sq. units (D) none of these
A. 2
B. `(9)/(4)`
C. `(9)/(3)`
D. `(9)/(2)`

Answer 1

Correct Answer - B
The area bounded by the curve `y^(2)=4x` Y-axis and line `y=3` is shown by shaded region in the figure.
` :.` Required area `=int_(0)^(3)xdy`
`=int_(0)^(3)(y^(2))/(4)dy`

`=(1)/(4)[(y^(3))/(3)]_(0)^(3)`
`=(1)/(12)(3^(3)-0)`
`=(1)/(2)(3^(3)-0)`
`=(1)/(12)(27)=(9)/(4)` sq. units.