Question

Integrate with respect to $t$.

$\int \left(4\cos t+t^2\right)dt$

• A. $4\sin t+\frac{t^3}{3}$
• B. $4\sin t-\frac{t^3}{3}$
• C. $4\sin t+2t$
• D. $4\sin t+t^3$

Answer 1

Answer: (A)

$4\sin t+\frac{t^3}{3}$

Let $I=\int \left(4\cos t+t^2\right)dt$

$=4\int \cos tdt+\int t^{2}dt$

$=4\sin t+\frac{t^3}{3}+c$