From the image, the problem asks to determine the total revenue (TR) function given the marginal revenue (MR) function:

$MR = f'(Q) = 5 - 3Q$

To find the total revenue function $TR(Q)$, we integrate the marginal revenue function with respect to $Q$:

$TR(Q) = \int MR \, dQ$

Steps:

1. Integrate $MR = 5 - 3Q$: $TR(Q) = \int (5 - 3Q) \, dQ = 5Q - \frac{3}{2}Q^2 + C$

2. The constant $C$ represents the initial revenue when $Q = 0$. If no initial condition is provided, $C$ remains as an unknown constant.

Final Answer:

$TR(Q) = 5Q - \frac{3}{2}Q^2 + C$

Let me know if you want further explanation or calculations!

Here are some follow-up questions to expand your understanding:

1. What is the economic meaning of the constant $C$ in the total revenue function?
2. How would the total revenue function change if the marginal revenue had a quadratic term?
3. How do marginal revenue and total revenue relate graphically?
4. How do we determine the quantity $Q$ that maximizes total revenue?
5. What happens to $MR$ and $TR$ when $MR = 0$?

Tip: The integration process is essential in transitioning from marginal functions (rates of change) to total functions. Always remember to add the constant of integration!