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.

Answer 1

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