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Typical courses on real integration spend a lot of time defining the Lebesgue measure and then spend another lot of time defining the integral with respect to a measure. This is sometimes criticized ...

I'm teaching Calculus and my students asked me to calculate the integral of $\ x\! \cdot\!\tan(x)$. I spent quite a lot of effort to do this, but I'm now even not sure if the integral could be ...

What interesting applications are there for theorems or other results studied in first-year calculus courses? A good example for such an application would be using a calculus theorem to prove a ...