Question

The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is ______.

Options

• 4

• 2

• 3

• 1

Answer 1

The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is 1.

Explanation:

The required area is shown by shaded region

Required Area

A = `int_1^3|x - 2|dx = 2int_2^3(x - 2)dx`

= `2[x^2/2 - 2x]_2^3`

= 1