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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How to get to the closed form of $\int_{-\infty}^{\infty} \frac{x^2e^x}{(e^x+1)^2}$ [duplicate]

I came across this integral when helping some friends with a statistical mechanics assignment, Mathematica reports it as $\frac{\pi^2}{3}$. So far I have noticed that the integrand is an even ...
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Find the points on the curve $y=x+e^x$ at which the tangent line is horizontal.

Find the points on the curve $y=x+e^x$ at which the tangent line is horizontal. The answer was $(0,1)$, but I don't get it. I tried to take the derivative of the function and equal it to $0$ ...
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Triple Integral with spherical polar coordianates [on hold]

By changing into spherical coordinates (or by any other method) evaluate the triple integral $$\iiint_V xyz \ dxdydz,$$ where $V$ is the volume in $\mathbb{R}^3$ deifned by the inequalities ...
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evaluating $\int_0^\infty \int_y^\infty y^2e^{-x^4} \ dx \ dy$

evaluating $\int_0^\infty \int_y^\infty y^2e^{-x^4} \ dx \ dy$ my book states $$\int_0^\infty \int_y^\infty y^2e^{-x^4} \ dx \ dy = \int_0^\infty \int_0^x y^2e^{-x^4} \ dy \ dx$$ Could someone ...
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Natural Logs and Anit-Derivatives are kicking me

I am given a problem involving rates of flow, $F(t)=\frac{t+7}{2+t}$ is the rate at which a bucket is being filled. The same bucket is being emptied at a rate given by $E(t)=\frac{\ln(t+4)}{t+2}$. My ...
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Extending the Riemann integral to any compact set

One basically defines a Riemann integral on a closed interval. I'd like to extend the Riemann integral to any compact set. Let $K \in \Bbb R$ be compact. Let $f\colon K \rightarrow \Bbb R$, with the ...
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Stoke's Theorem?

Let $S$ be the portion of the plane $x+y+z=1$ that lies in the first octant, and let C be the boundary of S, traversed counterclockwise. Calculate $\int_{C} F.dr$ where ...
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