# 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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### Resistance of a frustum, or a pyramid cut from top

We know that Resistance is given by: $$R = \dfrac{\rho L}{A}$$ The figure of Resistance is like this, $L$ is perpendicular distance between $A_1$ and $A_2$ I assumed that the area change linearly, ...
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### Alternate proof of the dominated convergence theorem by applying Fatou's lemma to $2g - |f_n - f|$?

Here is a proof of the dominated convergence theorem. Theorem. Suppose that $f_n$ are measurable real-valued functions and $f_n(x) \to f(x)$ for each $x$. Suppose there exists a nonnegative ...
### What is the value of $I=\lim_{n \to \infty} \int_0^1 {{1 + nx^2}\over{(1 + x^2)^n}} \log(2 + \cos(x/n))\,dx.$?
Find the integral $I$.....it looks like a good problem which I was not able to solve ....please help... $$I=\lim_{n \to \infty} \int_0^1 {{1 + nx^2}\over{(1 + x^2)^n}} \log(2 + \cos(x/n))\,dx.$$