Question

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
g(t) =
4 + t + t2

t

G(t) =

Answer 1

Step-by-step explanation:

$G(t) =\displaystyle \int (4 + t + t^2)dt$

$\:\:\:\:\:\:\:=4t + \frac{1}{2}t^2 + \frac{1}{3}t^3 + C$

Check:

$\dfrac{d}{dt}(4t + \frac{1}{2}t^2 + \frac{1}{3}t^3+C)= 4 + t + t^2 =g(t)$