# Tagged Questions

Concerns all aspects of integration, including the integral definition and computational methods. For questions solely about the properties of integrals, use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that typically describe(s) the types of ...

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### Proving that an infinite series equal a finite series

Suppose we have a function $f(z)$, which has $m$ isolated singularities, which are non-integers (say, $z_1$, $z_2$,...,$z_m$). Define $H(z):=\frac{\pi f(z)}{\sin(\pi z)}$. Assume that there exists a ...
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### Does it follow that $\{f_n\}$ is uniformly integrable?

Suppose $\mu$ is a finite measure, $f_n \to f$ almost everywhere, each $f_n$ is integrable, $f$ is integrable, and $\int |f_n - f| \to 0$. Does it follow that $\{f_n\}$ is uniformly integrable?
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### Integral of the level curve $ye^{2x}$

$\int_{0}^{2}\int_{0}^{4} ye^{2x}$ $dydx$ The book says the answer is $32(e^4-1)$ I had to do u-substitution when doing it, maybe that's where I went wrong. First integrating with respect to y, ...
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### L^1 convergence and limsup of convergent sequence

I have to solve this exercise: let $f_n$ be a sequence of positive real function defined on a measure space $(X,M,\mu)$ such that $f_n\in L^1(\mu)$ $\forall n\in \mathbb{N}$ and $f_n$ is convergent in ...
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### how do I integrate a modulus function. is it possible?

I am solving a question in which after calculating, my instantaneous velocity is $f(t)=\frac{ab\sin(bt)}{\sqrt{2-2\cos(bt)}}$. So I need to find distance in time $T$. For finding distance I need to ...
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### what is the solution of $\int e^{-3} . x^{-3} dx$?

What is the integration of $\int e^{-3} . x^{-3} dx$ and how to derive it?
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### Limit of an integral involving the floor function

I am trying to obtain an asymptotic expansion of $$\int_t^\infty \lfloor x\rfloor \frac {x}{\sqrt{x^2-t^2}} \ \Bbb d x$$ for $t \to \infty$ and $\lfloor x \rfloor$ denoting the floor function. I ...
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### Definite integrals evaluation

I have two results:  $\int_2^3f(x)dx=5$ and $\int_1^2 xf(x^2-1)dx=8$ I need to calculate: $$\int_0^2 f(x)dx$$ I have no idea about using the previous results, any hint?
### Finding $\int \frac{\mathrm{d}x}{1 + \frac{2}{x} - x}$
I want to solve: $$\int\frac{1}{1+\frac{2}{x}-x} \mathrm{d}x$$ I don't know how to start, maybe I should use partial fraction?