Question:
Find the value of \(\displaystyle\int_2^3\dfrac1x\,dx\).
Find the value of \(\displaystyle\int_2^3\dfrac1x\,dx\).
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The antiderivative of 1/x is ln|x|; evaluate at the limits and subtract.
Updated On: Sep 23, 2026
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Solution and Explanation
Step 1: Find the antiderivative:
\(\displaystyle\int\dfrac1x\,dx=\ln|x|+C\).
Step 2: Apply the limits:
\[ \int_2^3\dfrac1x\,dx=\ln3-\ln2=\ln\dfrac32 \]
Final Answer:
\[ \boxed{\ln\dfrac32} \]
\(\displaystyle\int\dfrac1x\,dx=\ln|x|+C\).
Step 2: Apply the limits:
\[ \int_2^3\dfrac1x\,dx=\ln3-\ln2=\ln\dfrac32 \]
Final Answer:
\[ \boxed{\ln\dfrac32} \]
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