Question

Find the area of the region bounded by the curve y = x², and the lines x = 1, x = 2, and y = 0.

Answer 1

Given:

y = x², x = 1, x = 2, y = 0

Let A be the required area

Area of region = `int_1^2 ydx`

= `int_1^2 x^2dx`

= `[x^3/3]_1^2`

= `1/3`[2³ - 1³]

= `1/3`[8 - 1]

= `7/3`

Therefore, the required area = `7/3` square units.