Question

If `int_0^a 3x^2 dx = 8` then a = ______.

Options

• 0

• 2

• 8

• `4/3`

Answer 1

If `int_0^a 3x^2 dx = 8` then a = 2.

Explanation:

`int_0^a 3x^2 dx`

`int x^n dx = x^(n + 1)/(n + 1)`

`int 3x^2 dx = 3 * x^3/3`

= x³

`[x^3]_0^a` = 8

a³ − 0³ = 8

a³ = 8

Taking the cube root of both sides:

`a = root(3)(8)`

a = 2