Discussion
Integrating the reciprocal from one as far as \( e \) yields
Answer: C
The reciprocal integrates to the natural logarithm:
\[ \int_{1}^{e} \frac{dx}{x} \;=\; \left[\ln x\right]_{1}^{e} \;=\; \ln e - \ln 1 \;=\; 1 - 0 \;=\; 1. \]
This is the defining property of \( e \): it is the upper limit at which the area under the reciprocal curve, measured from one, first reaches unity
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