CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The marginal revenue of a firm is MR = 100 − 4x, where x is the number of units sold, and revenue is zero when nothing is sold. The total revenue function is:
The total revenue function is R = 100x − 2x². Integrating marginal revenue term by term gives 100x − 2x² plus a constant, and zero revenue at zero sales makes the constant zero.
- AR = 100x − 4x²
- BR = 100x − 2x²Correct
- CR = 100 − 2x²
- DR = 100x − 2x² + 100
Explanation
R = ∫(100 − 4x) dx = 100x − 2x² + k. Since R(0) = 0, k = 0. So R = 100x − 2x². The option 100x − 4x² forgets to divide by the new power 2.
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