Question

The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.

Options

• 21 sq units

• 10 sq units

• 20 sq units

• 21/2 sq units

Answer 1

The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is 21 sq units.

Explanation:

∴ Required area = Area of the shaded region

= `int_1^4 (-y) dx`

= `int_1^4 x^2 dx`

= `[x^3/3]_1^4`

= `64/3 - 1/3`

= `63/3`

= 21 sq units