## Fining the angular bounds of a triple integral function February 6

This problem requires the taking of a triple integral over a region. I believe it's most useful to convert to cylindrical coordinates, which I did. However, I could not find the theta bounds ...

## Can limits to definite integral be vectors February 6

There are two cases: 1-Limits are scalar and function to be integrated is vector.2- Limits are vector and function to be integrated is vector.Are both valid. If yes can you give example for each.Actually the problem is I have problem in which I have

## How to prove Integral result February 6    1

I am trying to solve a integral through Mathematica, Mathematica gives me the following answer My question is how to solve this integral manually to get the Mathematica result or can we prov ...

I would like to compute $\displaystyle I=\int_0^{+\infty}\frac{\arctan(t)}{e^{\pi t}-1}dt$ Let $D=(0,+\infty)$, I have $\frac{1}{e^{-\pi t}-1}=\frac{e^{-\pi t}}{1-e^{-\pi t}}$So $$\frac{\arctan(t)}{e^{\pi t}-1}=\sum_{k=1}^{+\infty}\arctan(t)e^{-k \pi ## Angular Velocity through integration February 6 1 How to integrate a\ddot\theta = \frac{gsin2\theta}{2}  to find r\dot\theta^2r is the radius. I am not sure how to integrate the equation with respect to t. Kindly explain.Start with$$\ddot\theta = \frac g {2a} \sin(2\theta)and multiply both si ## How to compute \int_0^1 \frac{x-1}{\ln(x)} dx = \ln(2) and \int_0^\infty \ln(t) e^{-t} dt  February 6 2 \int_0^1 \frac{x-1}{\ln(x)} dx = \ln(2)First i try \ln(x)=t so that \frac{1}{x} dx =dt then integral becomes \begin{align} &\int_{-\infty}^{0}\frac{e^t-1}{t} (e^t dt) = - \int_0^{\infty} \frac{e^{-t}-1}{t} e^{-t} dt = -\int_0^{\infty} (t^{-1} e ## Proving the problem of integration February 6 2 From a journal, they proved this equality: \frac{z}{\alpha -1}\left(\int_0^1 \frac{t^{\frac{1}{\alpha}}}{1-tz} dt -\alpha \int_0^1 \frac{v}{1-vz} dv\right) = \int_0^1 t^{\frac{1}{\alpha}} \left(\int_0^1 \frac{vz}{1-tvz}dv\right)dt $$I already tried ## Integration intuition question (integrating velocity from 0 to 1) closed February 6 1 I'm really confused because I started to get the hang of integration and this isn't making sense. If distance is equal to the sum of velocity times change in time, and when I try to integrate from 0 to 1 it doesn't work. Is there some special rule th ## integral of \ln x from 0 to 1 February 6 2 I have a question about the integral of \ln x.When I try to calculate the integral of \ln x from 0 to 1 I always get the following result.x(\ln x -1) (integral of \ln x)1(\ln 1 -1) - (0 (\ln 0 -1)) But the second part of the calculation is ## Reverse Power Rule integration. February 6 2 Ok, so I am confused about the following;When we have a polynomial, say P(x), and we want to solve an integral where P(x) is raised to a certain power, for example;$$\int (P(x))^adx$$Why can we not integrate it using the fact that integration is ## Compute \int_0^1 \frac{ 1}{1 + x^{1/2}}\,dx. February 6 Basically, the question is Compute$$\int_0^1 \frac{ 1}{1 + x^{1/2}}\,dx.$$I have no idea how to approach this and have spent hours to no avail. Any help would be gladly appreciated. Thanks!! ## integration of 1/x a counterexample to the rule February 6 We know that the integration of$$\int\frac{1}{x}=log(x)$$but if we go by normal rule then it becomes$$\infty$$is this a counterexample to the rule of x^{n+1}/(n+1) or am i missing something. You Might Also Like • Uniqueness principle theorem :If f and g are analytic functions on a domain D, and if f(z)=g(z) for ... • This may well be a stupid question. I'm currently trying to find out whether a production function I have ha ... • Consider two integers m and n, with m > n, and A, x and b real matrices and vectors. In the c ... • Let X be a random variable with variance Var[X]=\sigma^2. Given a number of (independent) realizations  ... • Suppose that a certain conference has a random number of attendees. The expected number of attendees is 100. ... • Hi I am trying to solve this double integral$$ I:=\int_0^\infty \int_0^\infty \frac{\log x \log y}{\sqrt {x ...
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