Question

`int_(-7)^7 x^3/(x^2 + 7) * dx` = ______.

Options

• 7

• 49

• 0

• `(7)/(2)`

Answer 1

`int_(-7)^7 x^3/(x^2 + 7) * dx` = 0.

Explanation:

A function f(x) is odd if:

f(−x) = −f(x)

Let f(x) = `x^3/(x^2 + 7)`

∴ f(– x) = `(-x)^3/((-x)^2 + 7)`

= `x^3/(x^2 + 7)`

= – f(x)
∴ f(x) is an odd function.