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Question
Using integration, find the area of the region in the first quadrant enclosed by the line x + y = 2, the parabola y2 = x and the x-axis.
Solution
Solving x + y = 2 and y2 = x simultaneously, we get the points of intersection as (1, 1) and (4, –2).
The required area = the shaded area = `int_0^1 sqrt(x) dx + int_1^2 (2 - x) dx`
= `2/3 [x^(3/2)]_0^1 + [2x - x^2/2]_1^2`
= `2/3 + 1/2 = 7/6` suqare units
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