CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If ∫ from 0 to k of (2x + 3) dx = 18, where k > 0, then the value of k is:
The integral from 0 to k of 2x + 3 equals k² + 3k. Setting this equal to 18 gives k² + 3k − 18 = 0, with roots 3 and −6. As k must be positive, k equals 3.
- A3Correct
- B2
- C6
- D−6
Explanation
∫ from 0 to k of (2x+3) dx = k² + 3k. Setting k² + 3k = 18 gives k² + 3k − 18 = 0, so (k+6)(k−3)=0, k = 3 or −6. Since k > 0, k = 3. The root −6 is rejected because k is positive.
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