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Area of the region bounded by the curve y2=4x, y-axis and the line y = 3 is: -

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Question

Area of the region bounded by the curve `y^2 = 4x`, `y`-axis and the line `y` = 3 is:

Options

  • 2

  • `9/4`

  • `9/3`

  • `9/2`

MCQ

Solution

`9/4`

Explanation:

The curve `y^2 = 4x` is the parabola MP is the line `y` = 3.

The area of the region bounced by `y^2 = 4x` and `y` = 3 is

`(y^2 = 4x : x = y^2/4)`

A = `int_0^3 x  dy`

= `int_0^3 y^2/4  dy = [y^3/1^2]_0^3 = 27/12 = 9/4`

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