Monday, October 6, 2014

Advanced Math Solutions – Integral Calculator, substitution

In the previous post we covered common integrals. You will find it extremely handy here b/c substitution is all about simplification, transforming the function into something more familiar.
At its basic form, substitution is used when an integral contains some function and its derivative. It is the reverse chain rule (click here for a quick review).

The substation rule is as follows:
\int f\left(g\left(x\right)\right)g^'\left(x\right)dx=\int f\left(u\right)du,\:\:\:where\:u=g\left(x\right)

Let’s see how it works, starting with the logarithmic function (click here):


Here’s an example of exponential functions (click here):


Here’s an example using the power rule (click here):



Here’s an example using simple trig substitution (click here):


Sometimes the appropriate substitution is not that obvious and requires some extra work.  We’ll walk you through more advanced examples in the next post

Cheers,
Michal

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