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

Explanation:

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

`\:\:\:\:\:\:\:=4t + (1)/(2)t^2 + (1)/(3)t^3 + C`

Check:

`(d)/(dt)(4t + (1)/(2)t^2 + (1)/(3)t^3+C)= 4 + t + t^2 =g(t)`