Integration by Substitution

(An archive question of the week) Last time, we looked at a method of integration, namely partial fractions, so it seems appropriate to find something about another method of integration (this one more specifically part of calculus rather than algebra). We will look at a question about integration by substitution; as a bonus, I will …

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Partial Fractions: How and Why

I have often noted that calculus class is where you really learn algebra. Certain techniques in calculus demand algebraic skills that either were not taught in algebra classes (because they are not needed until you get to calculus), or have been forgotten. Chief among these is the method of partial fractions. I have here put …

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Ranges of Inverse Trig Functions

(Archive Question of the Week) We have had a number of questions over the years about inverse trig functions and their ranges. For today’s question, I have chosen one from 2011, which will link to a number of others that I will not quote in detail.