Question

The area of the region bounded by the curve y = 2x - x² and the line y = x is ______ square units.

Options

• `1/6`

• `1/2`

• `1/3`

• `7/6`

Answer 1

The area of the region bounded by the curve y = 2x - x² and the line y = x is `underline(1/6)` square units.

Explanation:

The intersection points of given curves are (0, 0) and (1, 1).

∴ Required area = `int_0^1 [(2x - x^2) - x]`dx

`= int_0^1 (x - x^2) "dx" = [x^2/2 - x^3/3]_0^1`

`= 1/6`sq.unit