CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The value of the definite integral of 1/x with respect to x from x = 1 to x = e² is:
The integral of 1/x is the natural logarithm of x. Evaluating between 1 and e² gives ln(e²) minus ln(1), which is 2 minus 0, so the value of the definite integral is 2.
- A1
- B2Correct
- Ce²
- De² − 1
Explanation
The integral of 1/x is log x. Evaluating from 1 to e² gives log(e²) − log(1) = 2 − 0 = 2. Option e² − 1 wrongly treats the integrand as a constant (it is the result of integrating 1 over the interval).
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