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Question
Find the area of the region bounded by the curve y2 = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.
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Solution
Let A be the required area.
A = `int_1^4 y dx`
= `int_1^4 2sqrt(x) dx`
= `2 int_1^4 x^(1/2) dx`
= `2 . 2/3 [x^(3/2)]_1^4`
= `4/3 [4^(3/2) - 1]`
A = `28/3` sq. units.
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