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The area under \( y = 1/x \) from \( x = 1 \) to \( x = 4 \) is

  • A.\( \ln 3 \)
  • B.\( \ln 4 \)
  • C.\( 3 \)
  • D.\( 1/4 \)

Answer: B

The reciprocal integrates to a logarithm, and the difference of logarithms is the logarithm of the ratio:

\[ \int_{1}^{4}\frac{dx}{x} \;=\; \left[\ln x\right]_{1}^{4} \;=\; \ln 4 - \ln 1 \;=\; \ln 4 \;\approx\; 1.386. \]

The value \( \ln 3 \) would arise from taking the difference of the limits inside the logarithm rather than their ratio

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