Question

Using integration find the area of the region: 

{(x, y) : 0 ≤ y ≤ x², 0 ≤ y ≤ x, 0 ≤ x ≤ 2}

Answer 1

Area of the shaded region = `int_0^1 x^2dx + int_1^2 xdx`

= `[x^3/3]_0^1 + [x^2/2]_1^2`

= `[1/3 - 0/3] + [2 - 1/2]`

= `1/3 + 3/2`

= `(2 + 9)/6`

= `11/6` sq. unit