Question

`int_0^1 (x^4 - 1)/(x^2 + 1)` dx is equal to ______.

Options

• `2/3`

• `1/3`

• `(-2)/3`

• 0

Answer 1

`int_0^1 (x^4 - 1)/(x^2 + 1)` dx is equal to `underlinebb((-2)/3)`.

Explanation:

`I = int_0^1 (x^4 - 1)/(x^2 + 1) dx`

⇒ `I = int_0^1 ((x^2)^2 - (1)^2)/(x^2 + 1) dx`

⇒ `I = int_0^1 ((x^2 + 1)(x^2 - 1))/((x^2 + 1)) dx`

⇒ `I = int_0^1 (x^2 - 1) dx`

⇒ `I = [x^3/3 - x]_0^1`

= `1/3 - 1`

= `(-2)/3`