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 →
Insight Things
A scientific blog revealing the hidden links which shape our world
Tag: integration
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]](http://s0.wp.com/latex.php?latex=%5Ba%2Cb%5D&bg=ffffff&fg=000000&s=0 "[a,b]")
![\displaystyle s=\int\limits_{a}^{b}\sqrt{1+\big[f'(x)\big]^{2}}\,dx](http://s0.wp.com/latex.php?latex=%5Cdisplaystyle+s%3D%5Cint%5Climits_%7Ba%7D%5E%7Bb%7D%5Csqrt%7B1%2B%5Cbig%5Bf%27%28x%29%5Cbig%5D%5E%7B2%7D%7D%5C%2Cdx+&bg=ffffff&fg=000000&s=0 "\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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