CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
Evaluate the definite integral ∫₀² (6x² + 4x) dx.
The antiderivative of 6x² + 4x is 2x³ + 2x². Evaluating from 0 to 2: [2(2)³ + 2(2)²] − 0 = 16 + 4 = 20, using the Fundamental Theorem of Calculus.
- A12
- B16
- C20Correct
- D24
Explanation
First, find the antiderivative: ∫(6x² + 4x)dx = 2x³ + 2x² + C. Now evaluate from 0 to 2: [2x³ + 2x²]₀² = [2(8) + 2(4)] − [0] = 16 + 4 = 20. The distractor 16 omits the 2x² term contribution, and 24 results from arithmetic error in evaluating 2(8).
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