Question

The value of ${\int }_{-3}^3({ax}^5+{bx}^3+cx+k)dx$, where a, b, c, k are constant, depends only on

• A. a and k
• B. a and b
• C. a, b and c
• D. k

Answer 1

The correct option is D k

${\int }_{-3}^3({ax}^5+{bx}^3+cx+k)dx$
$={[\frac{{ax}^6}{6}+\frac{{bx}^4}{4}+\frac{{cx}^2}{2}+kx]}_{-3}^3$
$=\frac{a.3^6}{6}+\frac{b.3^4}{4}+\frac{c.3^2}{3}+k\left(3\right)-\frac{a.3^6}{6}-\frac{b.3^4}{4}-\frac{c.3^2}{3}+k\left(3\right)$
$=6k$
$\therefore$ Integral depends upon k.