1. ## Confused About Finding Function based on the Integral

I know that the function that is based on the integral is just done by taking the integral with our rules which get me (5/3)x^3 - 2x^2, but im not sure how im suppose to find the C value based on what's given?

Any guidance/explanation would be nice

2. ## Re: Confused About Finding Function based on the Integral

This is a definite integral. There is no added constant

\begin{align*} &\displaystyle \int_2^x (5t^2 - 4t)~dt = \\ &\left . \dfrac 5 3 t^3 - 2t^2 \right |_2^x = \\ &\left(\dfrac 5 3 x^3 - 2 x^2\right) - \left(\dfrac 5 3 2^3 - 2(2)^2\right) = \\ &\left(\dfrac 5 3 x^3 - 2 x^2\right) - \left(\dfrac{40}{3} - 8\right ) = \\ &\dfrac 5 3 x^3 - 2 x^2 - \dfrac{16}{3} \end{align*}