Question

The value of ${\int }_{-2}^2(a{x}^3+bx+c)dx$ depends on:

• A. The value of $b$
• B. The value of $c$
• C. The value of $a$
• D. The value of $a$ and $b$

Answer 1

Answer: (B)

The value of $c$

For an odd function $f\left(x\right)$, ${\int }_{-a}^{a}f\left(x\right)dx=0$

And, for an even function $g\left(x\right)$, ${\int }_{-a}^{a}g\left(x\right)dx=2{\int }_0^{a}g\left(x\right)dx$

Now, in the given integration, $a{x}^3$ and $bx$ are odd functions and hence their integration is 0.

Hence , integration becomes ${\int }_{-a}^{a}cdx=2{\int }_0^{a}cdx=2ca$

Hence, integration depends on $c$ only.