All Questions
Tagged with bounds-of-integration limits
4
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Conditions on a rate of change of a continuous function to be bounded
Suppose $f(s)$ is continuous on $[0,\infty)$ and $\lim_{s\to \infty} f(s) =1$. How fast should it decrease to $1$ so that $$F(t)=\int_0^t f(s)\sin(s)ds$$ to be bounded? In what cases it is ...
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Limit of ratio of incomplete gamma function
In order to derive Sterling's approximation, I need to show that the following integral decays quicker than at least $\mathcal{O}(n^2)$:
$\lim_{n\to\infty}\dfrac{\int_{2n}^\infty x^ne^{-x}dx}{\int_{0}^...
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Limits of bounded region
While solving a simple problem for finding are of the region bounded by $x=y^2$ and $x=y$. Are the following correct limits?
When $x$ is the outer integration variable
$$\int^1_0\int^\sqrt{x}_xdydx$$...
- 849
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Evaluating $\int_{-\infty}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x$
I am interested in the improper integral: $$I=\int_{-\infty}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x=2\int_{0}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x$$ which I am fairly sure converges.
I broke the integral ...
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