Question

Area of figure bounded by straight lines x = 0, x = 2 and the curves y = 2^x, y = 2x – x² is ______.

Options

• `3log_2e - 3/4`

• `3/(ℓ n2) - 4/3`

• `3/(ℓ n2) + 3/4`

• `3/(ℓ n2) + 4/3`

Answer 1

Area of figure bounded by straight lines x = 0, x = 2 and the curves y = 2^x, y = 2x – x² is `underlinebb(3/(ℓ n2) - 4/3)`.

Explanation:

A = `int_0^2 (2^x - 2x + x^2)dx`

= `[2^x/(ℓ n2)]_0^2 - (x^2)_0^2 + 1/3[x^3]_0^2`

= `3/(ℓ n2) - 4 + 8/3`

= `3/(ℓ n2) - 4/3`