Question

`int_(-5)^5  x^7/(x^4 + 10)  dx` = ______.

Options

• 10

• 5

• 0

• `1/5`

Answer 1

`int_(-5)^5  x^7/(x^4 + 10)  dx` = 0.

Explanation:

Let f(x) = `x^7/(x^4 + 10)`

∴ f(– x) = `(-x)^7/((-x)^4 + 10) = (-x^7)/(x^4 + 10)`

=  – f(x)

∵ f(– x) = – f(x)

∴ f(x) is an odd function

∴ `int_(-a)^a f(x).dx` = 0

⇒ `int_(-5)^5  x^7/(x^4 + 10)  dx` = 0