CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If the definite integral of (kx + 3) with respect to x from 0 to 2 equals 14, then the value of k is:
The value of k is 4. The integral of kx + 3 from 0 to 2 equals 2k + 6. Setting this equal to 14 gives 2k = 8, so k = 4, which checks because 2×4 + 6 equals 14.
- A4Correct
- B3
- C6
- D5
Explanation
∫₀² (kx + 3) dx = [kx²/2 + 3x] from 0 to 2 = 2k + 6. Setting 2k + 6 = 14 gives k = 4. Check: 2(4) + 6 = 14. Option 3 would give 12 and 5 would give 16.
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