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Question
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.
Options
2
`9/4`
`9/3`
`9/2`
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Solution
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is `underline(9/4)`.
Explanation:
Equation of the curve y = 4x
This is the equation of a parabola whose centre is the origin.
Required ocean = Ocean of AOB
`int_0^3 x dy`
`= int_0^3 y^2/4 dy ....(because y^2 = 4x)`
`= [y^3/12]_0^3 = [27/12 - 0]`
`= 27/12`
`= 9/4` square unit
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