Search any question & find its solution
Question:
Answered & Verified by Expert
The value of $\int_{-2}^{2}\left(a x^{3}+b x+c\right) d x$ depends on the
Options:
Solution:
2053 Upvotes
Verified Answer
The correct answer is:
value of
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 .
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.