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 calculus
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.
The use of trigonometric identities to rephrase problems in Calculus is a very important skill. In this limits problem, it really really helps!
Sometimes, limit problems can be difficult. This is one such limit where an advanced factoring trick unlocks the solution.
Sometimes there are multiple ways to do a problem. This one can be approached somewhat systematically, with intuition helping us out.
Sometimes a Calculus problem is about non-obvious algebra. Here is one such instance. Let’s get into it!
For Calculus students, this topic can be very tricky. Here is a discussion that can help.
Integration rules are simple. Sometimes, the rules show up in very interesting ways.
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!
Here is a link to a Desmos workbook I made that allows us to decompose any function into its odd and even components. Super useful for various integration problems in Calculus.
Papa Flammy isn’t kidding. This is an absolutely beautiful result, as is the path to getting there.
Here is a problem from a first-year DiffEq class with a straightforward solution.
Having a look at the machinations of how solving problems works sometimes results in a deeper understanding of what solving certain types of problems is all about. This differential equation problem is interesting, in that regard.
Sometimes we need some combination of multiple integration techniques to solve an integration problem. Here is one such case, featuring a rational function.