Question

\(\displaystyle \int x\,(4x^{2}-6)\,dx=\) ?

• A. \(4x^{3}-6x+k\)
• B. \(\dfrac{4x^{4}}{3}-6x^{2}+k\)
• C. \(x^{4}-3x^{2}+k\)
• D. \(\dfrac{4x^{3}}{3}-3x^{2}+k\)

Hint:

Always simplify the integrand (expand/factor) before integrating.

Answer 1

The Correct Option is C

First expand: \(x(4x^{2}-6)=4x^{3}-6x\). Integrate termwise: \[ \int 4x^{3}dx=x^{4}, \int -6x\,dx=-3x^{2}. \] Hence \(x^{4}-3x^{2}+k\).