Insight Things

A scientific blog revealing the hidden links which shape our world

Tag: integration

Integration by Substitution – Why it works!

Integration by substitution (often referred to as u-substitution) is quite hard to understand. Most people just follow their proven recipe when performing this kind of integration. In contrast to that doing, I want to illustrate why the steps of u-integration are necessary. Therefore we will develop the idea slowly by giving simple examples which illustrate what works and what doesn’t. more →

Arc length of a function

There are many applications for the arc length of functions. I came across it when I needed to calculate the length of a density function in an interval [a,b]. The formula reads

\displaystyle s=\int\limits_{a}^{b}\sqrt{1+\big[f'(x)\big]^{2}}\,dx

Do you grasp how this formula arises? No? Let me show you! more →

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