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Question
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
Solution
Given equation of the parabola is y2 = 25x
∴ y = `5sqrt(x)` ......[∵ In first quadrant, y > 0]
Required area = area of the region OQRPO
= 2 (area of the region ORPO)
= `2 int_0^5 y "d"x`
= `2 int_0^5 5sqrt(x) "d"x`
= `10 int_0^5 x^(1/2) "d"x`
= `10[(x^(3/2))/(3/2)]_0^5`
= `20/5[(5)^(3/2) - 0]`
= `20/3 (5sqrt(5))`
= `(100sqrt(5))/3` sq.units
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