Question

Prove that: ${\int }_{-1}^1(a{x}^3+bx)dx=0$ .

Answer 1

${\int }_{-1}^1(a{x}^3+bx)dx=0$
Since, $f\left(x\right)=a{x}^3+bx$ is an odd function. So its value within the given limit will always be O.
Hence, this holds for any values of a and b.