Solve the integral: \int_0^2\frac{dx}{\sqrt{x}(x-1)}



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Solve the integral:

Answer & Explanation



Beginner2022-01-06Added 27 answers

You can break up the integral at any point or points you like. In this case, you could break it up into three integrals: pick a point c strictly between 0 and 1, and consider:
The original improper integral exists if and only if each of the three improper integrals exist.
Jenny Bolton

Jenny Bolton

Beginner2022-01-07Added 32 answers

Consider the change of variables t=x. It transforms the interval [0,2] into [0,2] and removes one of the problem zeroes. It is easy to see from the resulting expression that the integral diverges.


Expert2022-01-11Added 613 answers

Try to solve the integral. You'll find whether it converges. For example, dxx(1x) with ϵ>0. Later on, you can study the limit ϵ0+. In this way, you ''kill two birds with a one shot''.

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