Question

Find the area bounded by the curve y = |x – 1| and y = 1, using integration.

Answer 1

We have, y = (x – 1)

y = x – 1, if x – 1 ≥ 0

y = –x + 1, if x – 1 < 0

Required Area = Area of shaded region

A = `int_0^2 ydx`

= `int_0^1(1 - x)dx + int_1^2(x - 1)dx`

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

= `(1 - 1/2) - (0 - 0/2) + (4/2 - 2) - (1/2 - 1)`

= `1/2 + 1/2`

= 1 sq.unit