Question

${\int }_{-1}^1(a{x}^3+bx)dx=0$ for

• A. any values of $a$ and $b$
• B. $a>0$ and $b>0$ only
• C. $a>0$ and $b<0$ only
• D. $a<0$ and $b<0$ only

Answer 1

The correct option is A any values of $a$ and $b$

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