Q. The value of $\int_{- 3}^{3}{\left( ax^{5} + bx^{3} + cx + k \right)dx}$, where $a,b,c,k$ are constant, depends only on
A) $a\ and\ k$
B) $a\ and\ b$
C) $a,b\ and\ c$
D) $k$
Explanation
(d)
$\int_{- 3}^{3}{(ax^{5} + bx^{3} + cx + k)}dx$
$= \left\lbrack \frac{ax^{6}}{6} + \frac{bx^{4}}{4} + \frac{cx^{2}}{2} + kx \right\rbrack_{- 3}^{3}$
$= \frac{a.3^{6}}{6} + \frac{b.3^{4}}{4} + \frac{c.3^{2}}{3} + k(3) - \frac{a.3^{6}}{6} - \frac{b.3^{4}}{4} - \frac{c.3^{2}}{3} + k(3)$
$= 6k$
$ie$, Integral depends upon $k$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.