CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The rate of change of revenue is R'(x) = 100 − 4x (in ₹), where x is units sold, and revenue is zero when no units are sold. The total revenue from selling the first 10 units is:
Total revenue from the first 10 units is the integral of marginal revenue from 0 to 10. The antiderivative 100x − 2x² gives 1000 − 200 = 800, so total revenue is ₹800.
- A₹800Correct
- B₹1,000
- C₹600
- D₹400
Explanation
Revenue = ∫ from 0 to 10 of (100 − 4x) dx = [100x − 2x²] = 1000 − 200 = 800. The value 1,000 ignores the −4x term's contribution. Value 600 would come from using 3x² type mistakes, but 2x² is correct.
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