CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
Evaluate ∫₁⁴ (3√x) dx.
The value is 14. The antiderivative of 3√x is 2x^(3/2). Evaluating at the upper limit 4 gives 16 and at the lower limit 1 gives 2, so the definite integral is 16 − 2 = 14.
- A14Correct
- B7
- C28
- D16
Explanation
∫3x^(1/2)dx = 3·x^(3/2)/(3/2) = 2x^(3/2). At 4: 2·8 = 16. At 1: 2·1 = 2. Difference = 14. The value 16 results from ignoring the lower limit.
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