How do I get $$ \int_a^b \frac{1}{x}dx = \ln\left(\frac{b}{a}\right)$$ as a limit of sum. The constant width partition of the interval $(a,b)$ doesn't seem to work.
Integral as a limit of a sum
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integration
limits
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0What makes you think the fixed-width Riemann sum doesn't work in the limit? – 2012-06-22
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2Typically the logarithm is *defined* $\log t:= \int_1^t\frac{1}{x}dx$, so your question follows nearly by definition. – 2012-06-22
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0@Anon I tried it but couldn't get to the answer. – 2012-06-22
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0@PrakashGautam Write up what you tried below your question. – 2012-06-22