Proving an integral existence using the principle of mathematical induction.

We can use the principle of mathematical induction to to show the existence of Some integrals. One key idea here is that we need to find a link between the induction hypothesis and what we want to prove. In our case here, the principle of mathematical induction will be useful. So we're going to prove that the statement that we have here is true for one. And after that we assume that our statement is true for n. And we want to prove that it's true for n plus one. Okay, we're gonna find a link between the Fn and FN Plus one. That means we want to find a link between the induction hypothesis and the statement that we want to prove that's for n plus one. Once we do that, we can conclude using the principle of mathematical induction that our statement is true. So in our case now we are using an integral. This integral is convergent, it does exist. So we now that it does exist because we can prove that it does exist all the time. We can use any Criterion that we now like the It bonded, we can bound the integral and child that it's, it is always bounded and therefore it does exist, Okay? And in our case here, we can prove easily that these integral is convergent. Okay? This is an improper integral of the first kind. So we know how to deal with improper integrals of the first sky. The use of the principle of mathematical induction is very critical. It does help us prove some results that we can't do. So, in our case here, we can easily prove that our integral exists. We can also find the value of this. Integral, The principle of mathematical induction is very useful and its applicable. We have defined in the last videos. What we mean by the principle of mathematical. Induction, We have given proofs and results concerning that.
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