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Free study guides and discussions about various topics in Mathematics. Thanks for stopping by!

A free Odd-Even function workbook - now on Desmos!

All my readers know that Desmos is my favorite graphing calculator of all time. I have been working on a couple of Calculus articles that involve integration techniques where we consider the odd-even properties of integrands.

As covered in a previous article, recall that any function, $f(x)$, can be decomposed into its odd and even components, via: $$f_{e}(x) = \dfrac{1}{2}\bigg(f(x)+f(-x)\bigg)$$ and $$f_{o}(x) = \dfrac{1}{2}\bigg(f(x)-f(-x)\bigg)$$

Please also note that, we need only calculate the odd or even component of a function; to get the other, we just subtract the component from $f(x)$. For example (and this is how I do it in my Desmos workbook), if we calculate the even component of $f(x)$, all we need to do to calculate the odd component is to subtract the even component from $f(x)$, as: $$f_{o}(x)=f(x)-f_{e}(x)$$

Since I have been decomposing functions in this way using Desmos, I have made my workbook available via this link: https://www.desmos.com/calculator/fwytyc62vu. Please have a look and please use it. Let me know how it goes!

A tough trigonometric integral, solved multiple ways

My favorite math video right now