Q101 / 180 · KCET 2008 · Mathematics
The value of $\int_{-2}^{2}\left(a x^{3}+b x+c\right) d x$ depends on the
- Avalue of
- Correct answerBvalue of
- Cvalue of
- Dvalues of and
Solution
Let $\mathrm{I}=\int_{-2}^{2}\left(a x^{3}+b x+c\right) d x$
We know,
$$
\int_{-a}^{a} f(x) d x=\left\{\begin{aligned}
2 \int_{0}^{a} f(x) d x, & \text { if } f(-x)=f(x) \\
0, & \text { if } f(-x)=-f(x)
\end{aligned}\right.
$$
In the given integral, $a x^{3}$ and bx are odd functions.
Hence, it depends only on the value of .
Hence, the correct answer is option: 'B'.