# Tagged Questions

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### What is the geometric meaning of this integral?

In my math book, there is an exercise where the task is to compute the following integral and to interpret the result geometrically: $$\int_0^\pi\cos mx \cos nx \ dx$$ where $m,n \in \mathbb{N}$. ...
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### A difficult integral over matrix exponents - is there an analytical solution?

In short, I'm trying to find some method, apart from numerically integrating, to find the value of $$\bar{X}_t = \int_0^t e^{A^T (t-s)} Q e^{As} ds,$$ where $Q$ is ...
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### An integral problem related to matrix determinant

I am stuck in an integral problem: ...
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### Prove that the Laplace trasform is a Linear trasformation

Could you help me prove that the Laplace Trasform is a Linear trasformation? Thank you.
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### Any way to simplify the matrix integral $\int_{0}^{\infty}e^{A z}e^{B z}dz$ if A and B do not commute but are diagonalizable>

Define $A$ and $B$ square matrices where all eigenvalues are $< 0$ for both, and there is no eigenvalue multiplicity. Completely diagonalizable, etc. But assume that $A$ and $B$ do not commute. ...
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### Floating Point Number System

I really have no idea of how to do these questions - in fact I have no idea of how to do any question in the paper - but I have tried to figure out what's going on in the course called Computational ...
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### Surjectivity of an integration map

N.B.: Thanks to studiosus answer I realised I should ask for more conditions or otherwise the answer is straightforwardly wrong. I rechecked my problem and added new assumptions that I boldface. ...
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### Can I solve an integral (or other tough problem) by playing with knots?

I've seen that in calculating things in knot theory that involves a lot of hard looking integrals and matrices, even though the knots themselves appear fairly simple. So is there some way in which ...