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A concert promoter sells tickets and has a marginal-profit function given below, where P'(x) is in dollars per ticket. This means that the rate of
change of total profit with respect to the number of tickets sold, x, is P'(x). Find the total profit from the sale of the first 380 tickets, disregarding any
fixed costs.
P'(x) = 2x - 1198
The total profit is $

Respuesta :

Answer:

The answer is "-310840".

Step-by-step explanation:

[tex]\begin{array}{l} P'(x) = 2x - 1198\\ \\ \frac{{dP}}{{dx}} = 2x - 1198\\ \\ dP = \left( {2x - 1198} \right)dx\\ \\ \int {dP} = \int\limits_0^{380} {\left( {2x - 1198} \right)dx} \\ \\ P = \left( {2\frac{{{x^2}}}{2} - 1198x} \right)_0^{380}\\ \\ P = {380^2} - 1198 \times 380 = 144400-455240=-310840\\ \end{array}[/tex]

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