Nov 14 - Integration with 1/x

Today introduced a new and important integration idea. Because we defined ln x to be the antiderivative of 1/t as x goes from 1 to x, we can generalize that to be

Integral of 1/x dx = ln |x| + C (this is correct!!!!)

This will appear in a variety of ways, often following a u-substitution. The main confusion to AVOID is to recognize that the integration rule is very specific - it has to be 1/x. The rule can not be generalized to

Integral of 1/f(x) dx = ln |f(x)| + C; (this is not correct!!!!)

The only f(x) in the denominator that yields a ln(x) in the antiderivative is a linear function.

We will talk about integrating with e^x tomorrow, and then the rest of the week will be spent practicing integration and differentiation. There is a test next Monday.

Thanks to Madeline for her notes from today.


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