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CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

The rate of net investment is I(t) = 6t² (in ₹ lakh per year), where t is time in years. The capital accumulated between the end of year 1 and the end of year 3 is:

The capital accumulated is ₹52 lakh. Integrating the investment rate 6t² gives 2t³. Its value at t = 3 is 54 and at t = 1 is 2, so the accumulation over the period is 54 minus 2, which equals ₹52 lakh.

  1. A₹54 lakh
  2. B₹52 lakhCorrect
  3. C₹26 lakh
  4. D₹78 lakh

Explanation

Capital formed = ∫ from 1 to 3 of 6t² dt = [2t³] = 2(27) − 2(1) = 54 − 2 = 52. Option ₹54 lakh ignores the lower limit; ₹26 lakh halves the result by mistake.

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