Questions tagged [bounds-of-integration]
In many questions the problem of determining bounds of integration in multiple integrals is a major part of what an answer needs to deal with, and in surprisingly many questions it is the only issue. This tag is for such occasions.
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Bounds for the Harmonic k-th partial sum.
I need to bound the k-th partial sum or the Harmonic series. i.e.
$$ln(k+1)<\sum_{m=1}^{k}\frac{1}{m}<1+ln(k)$$
I'm triying to integrate in $[m,m+1]$ in the relation $\frac{1}{m+1}<\frac{1}...
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How can you simplify/verify this solution for $\int\limits_0^{.25991…} Q^{-1}(x,x,x)dx?$
As I do not know the complex behavior of this function, it would be even harder to integrate past the real domain. The upper bound for the domain is a constant I will denote β.
$${{Q_2}=\int_0^βQ^{-1}(...
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When is $\int_a^b \frac{1}{x}\ln\bigg(\frac{x^3+1}{x^2+1}\bigg)dx=0$?
I would like to find positive, distinct, algebraic real numbers $a,b\in \mathbb R^+\cap\mathbb A$ satisfying
$$\int_a^b \frac{1}{x}\ln\bigg(\frac{x^3+1}{x^2+1}\bigg)dx=0$$
Does anyone know of a ...
