Skip to content

CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

Which of the following is the value of the definite integral of (4x³ − 2x) with respect to x from x = 1 to x = 3?

The value is 72. The antiderivative of 4x³ − 2x is x⁴ − x². Evaluating at the upper limit 3 gives 72 and at the lower limit 1 gives 0, so the definite integral equals 72 minus 0, which is 72.

  1. A60Correct
  2. B68
  3. C72
  4. D64

Explanation

Antiderivative is x⁴ − x². At x = 3: 81 − 9 = 72. At x = 1: 1 − 1 = 0. The difference is 72 − 0 = 72. Hence the value is 72, not 60. Option 60 would result from using 81 − 9 − 12 incorrectly; 68 and 64 come from arithmetic slips.

Did you get it right without looking?

One question tells you little. A timed set on Differential and Integral Calculus shows your real accuracy, how long you take and where you lose marks.

Practise Differential and Integral CalculusFree diagnostic mock

More Differential and Integral Calculus questions