Final answer:
To find the total revenue function from the given marginal revenue (MR) function MR=10x-5x^2, we need to integrate MR with respect to 'x'. The resulting total revenue (TR) function is TR = 5x^2 - (5/3)x^3 + C, where C is the integration constant.
Step-by-step explanation:
The student is asking for the total revenue function, given the marginal revenue (MR) equation MR = 10x - 5x^2. To find the total revenue function, we need to integrate the marginal revenue function with respect to quantity, which is represented by 'x' here.
To integrate MR = 10x - 5x^2, we perform the integral operation on each term:
- The integral of 10x with respect to x is 5x^2.
- The integral of -5x^2 with respect to x is -5/3 * x^3.
The undetermined constant of integration will denote the constant part of the total revenue, which can be zero if the total revenue is also zero when the quantity is zero.
So the total revenue (TR) function is TR = 5x^2 - (5/3)x^3 + C, where C is the constant of integration.