Question

The area bounded by the curve | x | + y = 1 and X-axis is ______.

Options

• 1 sq unit

• 2 sq units

• 8 sq units

• None of these

Answer 1

The area bounded by the curve | x | + y = 1 and X-axis is 1 sq unit.

Explanation:

Given curve is | x | + y = 1

∴ Curve is x + y = 1, when x ≥ 0 and –x + y = 1, when x ≤ 0.

The graph of the given curve is shown below,

∴ Required area = Area CAOC + Area OABO

= `int_-1^0 y  dx + int_0^1 y  dx`

= `int_-1^0 (x + 1)  dx + int_0^1 (1 - x)  dx`

= `[x^2/2 + x]_-1^0 + [x - x^2/2]_0^1`

= `[0 - (1/2 - 1)] + [(1 - 1/2) - 0]`

= `1/2 + 1/2`

= 1 sq. unit