# Questions tagged [improper-integrals]

Questions involving improper integrals, defined as the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or $\infty$ or $-\infty$, or as both endpoints approach limits.

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### Fixed point iteration involving integral $f(x)=\int_{-\infty}^{\infty}k(x,t)f(x-t)dt+g(x)$.

Let $g(x)$ and $k(x,t)$ be two known functions. Is it possible to uniquely solve for $f(x)$ that is defined as: $$f(x)=\int_{-\infty}^{\infty}k(x,t)f(x-t)dt+g(x) \tag{1}$$ I am looking for a numerical ...
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### Why not expand the Lebesgue integral by summing up a series of multiple Lebesgue integrals? [duplicate]

Below is a classic example of an integral expression that can be computed using the improper Riemann integral, but not using the Lebesgue integral: $$\int\limits_0^\infty\frac{sin(x)}{x}$$ The problem ...
### Area between $\frac{\sin(x)}{x}$ and its derivative
I want to find the area of the space between $\frac{\sin{x}}{x}$ and its derivative, $\frac{x\cos(x)-\sin(x)}{x^2}$, that includes the origin. More specifically, between the sinc function and its ...