Question

`int_(-1)^1 (x + x^3)/(9 - x^2)  "d"x` = ______.

विकल्प

• 0

• 1

• `pi/4`

• `pi/2`

Answer 1

`int_(-1)^1 (x + x^3)/(9 - x^2)  "d"x` = 0.

Explanation:

Let f(x) = `(x + x^3)/(9 - x^2)`

∴ `"f"(- x) = (-x - x^3)/(9 - x^2)`

= `- (x + x^3)/(9 - x^2)`

= – f(x)

∴ f(x) is an odd function.

∴ `int_(-1)^1 (x + x^3)/(9 - x^2)  "d"x` = 0