Question

The area bounded by the x-axis and the curve y = 4x – x² – 3 is ______.

Options

• `1/3`

• `2/3`

• `4/3`

• `8/3`

Answer 1

The area bounded by the x-axis and the curve y = 4x – x² – 3 is `underlinebb(4/3)`.

Explanation:

y = 4x – x² – 3

⇒ x² – 4x + 3 = 0

⇒ (x – 3)(x – 1) = 0

⇒ x = 1, 3

A = `int_1^3(4x - x^2 - 3)dx`

= `[2x^2 - x^3/3 - 3x]_1^3`

= `18 - 9 - 9 - 2 + 1/3 + 3`

= `1 + 1/3`

= `4/3`