Question

The area bounded by y – 1 = |x|, y = 0 and |x| = `1/2` will be ______.

Options

• `3/4`

• `3/2`

• `5/4`

• None of these

Answer 1

The area bounded by y – 1 = |x|, y = 0 and |x| = `1/2` will be `underlinebb(5/4)`.

Explanation:

The given lines are,

y – 1 = x, x ≥ 0; y – 1 = – x, x < 0

y = 0; x = `-1/2`, x < 0; x = `1/2`, x ≥ 0

so that the area bounded is as shown in the figure.

Required area = `2int_0^(1//2) (1 + x)dx`

= `2(x + x^2/2)_0^(1//2) = 5/4`