Find the definite integral of int_{a}^{b} fra | vedclass

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(A) The integral of $\frac{1}{x}$ with respect to $x$ is $\log_{e} |x|$.Applying the fundamental theorem of calculus for the definite integral $\int_{

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$\log_{e} \left( \frac{b}{a} \right)$

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(A) The integral of $\frac{1}{x}$ with respect to $x$ is $\log_{e} |x|$.Applying the fundamental theorem of calculus for the definite integral $\int_{a}^{b} \frac{1}{x} dx$:$= [\log_{e} |x|]_{a}^{b}$$= \log_{e} |b| - \log_{e} |a|$Using the logarithmic property $\log_{e} m - \log_{e} n = \log_{e} \left( \frac{m}{n} \right)$:$= \log_{e} \left( \frac{b}{a} \right)$.

Find the definite integral of $\int_{a}^{b} \frac{1}{x} dx$.

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