Question

The value of `int_-3^3 ("a"x^5 + "b"x^3 + "c"x + "k")"dx"`, where a, b, c, k are constants, depends only on ______.

Options

• a, b and c

• k

• a and b

• a and k

Answer 1

The value of `int_-3^3 ("a"x^5 + "b"x^3 + "c"x + "k")"dx"`, where a, b, c, k are constants, depends only on k.

Explanation:

Let f(x) = ax⁵ + bx³ +cx

⇒ f(-x) = -ax⁵ - bx³ - cx = - f(x)

⇒ f(x) is an odd function.

∴ `int_-3^3 ("a"x^5 + "b"x^3 + "c"x)`dx = 0

∴ `int_-3^3 ("a"x^5 + "b"x^3 + "c"x + "k")`dx is depends only k.