Question

The value of `int_-1^1 (x^3)/(x^2 + 2|x| + 1) dx` is ______.

Options

• 0

• log 2

• 2 log 2

• `1/2` log 2

Answer 1

The value of `int_-1^1 (x^3)/(x^2 + 2|x| + 1) dx` is 0.

Explanation:

The denominator x² + 2|x| + 1 is an even function, since it contains x² and |x|. The numerator x³ is odd.

Hence, the integrand is odd.

The integral of an odd function over [−1, 1] is 0.