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Question
The area enclosed between the parabola y2 = 4x and line y = 2x is ______.
Options
`(2)/(3)` sq units
`(1)/(3)` sq unit
`(1)/(4)` sq unit
`(3)/(4)` sq unit
Solution
The area enclosed between the parabola y2 = 4x and line y = 2x is `bbunderline((1)/(3) "sq unit")`.
Explanation:
Area = `int_0^1 [2sqrt x - 2x]`
= `2[(x^(3//2))/(3/2) - x^2/2]_0^1`
= `2(2/3 - 1/2) xx 1`
= `4/3 - 1`
`1/3` sq. units.
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