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Question
Find the area of the region bounded by the curve y2 = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0
Solution
Let A be the required area.
Consider the equation y2 = 8x.
∴ A = `int_1^3 y "d"x`
= `int_1^3 sqrt(8x) "d"x`
= `2sqrt(2)[(x^(3/2))/(3/2)]_1^3`
= `(4sqrt(2))/3 [(3)^(3/2) - (1)^(3/2)]`
= `(4sqrt(2))/3 (3sqrt(3) - 1)` sq.units
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