CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
The rate of net saving of a country is S'(t) = 12t² rupees crore per year. The total saving accumulated between t = 0 and t = 2 years is:
Integrating the saving rate 12t² gives 4t³. Evaluating from 0 to 2 gives 4 × 8 = 32, so the accumulated saving is Rs 32 crore.
- ARs 48 crore
- BRs 24 crore
- CRs 32 croreCorrect
- DRs 16 crore
Explanation
∫ from 0 to 2 of 12t² dt = [4t³] from 0 to 2 = 4 × 8 = 32. Rs 48 results from using 12t³ without dividing by 3... actually 12×8/2 is not the rule; Rs 24 comes from wrongly using 12t²/... Both ignore dividing by the new power 3 properly.
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