The marginal revenue for a new calculator is given by , where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators.

Question

The marginal revenue for a new calculator is given by  , where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators. ​

Quizplus · Accepted Answer

To find the total revenue function, we need to integrate the marginal revenue function. Integrating 11ea984b_b172_5295_9029_65cb072f354c_TB4005_11 with respect to x gives:
R(x) = ∫(11x) dx = 11/2 x^2 + C
where C is the constant of integration. Since the revenue is 0 when the number of calculators is 0, we have:
0 = 11/2 (0)^2 + C
C = 0
Therefore, the total revenue function is:
R(x) = 11/2 x^2
which simplifies to:
R(x) = 5.5x^2
The closest choice to this function is option C: 11ea984b_b172_79a8_9029_7b6ead28ab20_TB4005_11.

The Marginal Revenue for a New Calculator Is Given by