CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
Evaluate ∫ from 1 to 2 of (3x² + 2/x) dx, with ln 2 = 0.693 (rounded to three decimals).
The value is 8.386. The integral of 3x² from 1 to 2 is 7, and the integral of 2/x is 2 ln 2, about 1.386. Adding these gives 8.386. Forgetting the coefficient 2 would wrongly give 7.693.
- A7.693
- B8.386Correct
- C6.307
- D7.000
Explanation
∫3x² dx = x³, giving 8 − 1 = 7 over the limits. ∫2/x dx = 2 ln x, giving 2 ln 2 = 1.386. Total = 7 + 1.386 = 8.386. The option 7.693 uses ln 2 instead of 2 ln 2, missing the coefficient 2.
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