Step 1: Identify the integral you need to calculate, which is ∫ from 0 to 1 of (1/x) dx.
Step 2: Recognize that the integral of (1/x) is ln(x).
Step 3: Set up the evaluation of the integral using the limits from 0 to 1: [ln(x)] from 0 to 1.
Step 4: Substitute the upper limit (1) into ln(x): ln(1) = 0.
Step 5: Substitute the lower limit (0) into ln(x): ln(0) is undefined and approaches negative infinity.
Step 6: Calculate the result: ln(1) - ln(0) = 0 - (-∞), which diverges.
Improper Integrals – The question tests understanding of improper integrals, particularly those that involve discontinuities or infinite limits.
Natural Logarithm Properties – It assesses knowledge of the properties of the natural logarithm, especially the behavior as the argument approaches zero.
