Seeing multiple ways to solve a problem is one of the beautiful things about using the tools of Mathematics in creative ways. This integral, done two different ways, reveals something interesting about two inverse trig functions.
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All tagged integration
Seeing multiple ways to solve a problem is one of the beautiful things about using the tools of Mathematics in creative ways. This integral, done two different ways, reveals something interesting about two inverse trig functions.
Integration rules are simple. Sometimes, the rules show up in very interesting ways.
A student brought this to a tutoring session recently. It's a really great question from the AP Calculus Exam prep materials. Nice one, College Board!
Another cool integration question from the front lines of Calc I / AP Calc.
This one is reduced to something super easy once we flex our integration muscles! King Property! Weierstrass substitution! Odd/even properties! Trig identities! One of my favorite articles to date!
Papa Flammy isn’t kidding. This is an absolutely beautiful result, as is the path to getting there.
Sometimes we need some combination of multiple integration techniques to solve an integration problem. Here is one such case, featuring a rational function.