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Area of the region bounded by the curve ...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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.
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