# Tagged Questions

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### How can I interchanging variables of integral in three dimensional

Given this integral $\int_0^1\int_0^{1-(y-1)^2}\int_0^{2-x}f(x,y,z)dzdxdy$ , how can I interchange the variables and express as integrals of the other five forms like dxdydz,dxdzdy...?? So what I ...
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### Using Mean Value Theorem for Integrals to prove Generalized MVT

The Mean Value Theorem for Integrals is $\int_Sf(x)g(x)dx$ =$f(c)\int_Sg(x)dx$ I am asked to use this to prove the generalized MVT which is $$\frac{f'(c)}{g'(c)}=\frac{f(b)-f(a)}{g(b)-g(a)}$$ how can ...
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### interchanging variables in triple integral

Give an integral $\int_0^1\int_0^{1-(y-1)^2}\int_0^{2-x}f(x,y,z)dzdxdy$ , how can I change to the format of dxdydz, dxdzdy, dydxdz, dydzdx, dzdxdy and dzdydx? So I figure out the region of the ...
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### describe triple integral algebraically and drawing

Describe the iterated integral $\int_0^1\int_0^{1-(y-1)^2}\int_0^{2-x}f(x,y,z)dzdxdy$ both by algebraically and drawing. That triple integral looks crazy for me.. how can I define a set that describe ...
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### Convergence of Improper Integral: $\int_{e^2}^\infty {dx\over x\log\log x}$

Test the convergence of the following integral$$\int_{e^2}^\infty {dx\over x\log\log x}$$ I understand that the problem is only at $\infty$ how to proceed ?
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### test convergence of improper integrals 4

Test the convergence of improper integrals : $$\int_1^2{\sqrt x\over \log x}dx$$ I basically have no idea how to approach a problem in which log appears. Need some hint on solving this type of ...
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### test for convergence of improper integral1

$$\int_0^1 {x^n\log x\over(1+x)^2} \, dx$$ I tried something using practical test, but not much progress. I see that the integral becomes improper for $x=0$, May be we need to apply the Practical ...
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### Is the improper integral $\int_0^\infty \frac{\ln x}{1+x^2}\,\mathrm dx$ convergent?

I would like to know if $$\int_{0}^{\infty}\frac{\ln x}{1+x^2}\,\mathrm dx$$ is convergent or divergent.
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### does $\intop_{1}^{\infty}x\sin(x^{3})dx$ really converge?

I'm trying to find a continuous function $f(x)$ on $[0,\infty)$ such that: $\intop_{1}^{\infty}f(x)dx$ converges while $f(x)$ isn't bounded. I came up with $f(x)=x\sin(x^{3})dx$, as a function ...
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### evaluating $\int_0^{\infty}\frac{e^{-t-\frac{x}{t}}}{t} dt$

I got to this integral, while proving some theorem in statistics: $$\int_0^\infty \frac{e^{-t-\frac{x}{t}}}{t} \mathop{dt}$$ I have trouble evaluating it. I tried partial integration, tried ...
### Improper Integral $\int_{1/e}^1 \frac{dx}{x\sqrt{\ln{(x)}}}$
I need some advice on how to evaluate it. $$\int\limits_\frac{1}{e}^1 \frac{dx}{x\sqrt{\ln{(x)}}}$$ Thanks!