KCET · Maths · Definite Integration
The value of \(\int_{-2}^{2}\left(a x^{3}+b x+c\right) d x\) depends on the
- A value of
- B value of
- C value of
- D values of and
Answer & Solution
Correct Answer
(B) value of
Step-by-step Solution
Detailed explanation
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 .
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 .
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