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in this video were gonna talk about three different applications of Taylor series three different things from back in calculus one in calculus two problems that either were challenging to do or that you couldnt do by the methods of calculus one in calculus two but now that we know Taylor series we can go back and do them the first of these Im going to focus on is an integration problem in particular consider the integral of e to the minus x squared DX and its actually a very important integral this kind of distribution and probability and statistics is called a normal distribution it comes up all the time so the issue of doing integrals of this form are actually pretty important but we dont know how to do that by the methods of calculus 1 or calculus 2 we get for example do a u sub it doesnt work out and youd want to try an integration by parts its not gonna be nice in fact it turns out that there isnt a nice answer in terms of functions like e to the X and polynomials and tr