# Tagged Questions

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### Integrate complex function

In a physics textbook I am working with, the following integral is caluclated: Define the complex elastic modulus as $\overline{M} = M_1 + i M_2$ where $\overline{M}$ is a function of the angular ...
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### show an integral is bounded by a constant independent of a parameter

This is a question in Treves. Suppose $a>1$ and $\tau \in \mathbb R$, (i) show that for all $(\tau, \xi) \in \mathbb R^{n+1}$, $|(\tau-ia)^2 - |\xi|^2| \ge(\tau ^2+|\xi|^2+a^2)^{1/2}$ (ii) ...
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### Compute the Integral

Compute the integral. $$\int_{-\infty}^\infty \frac{x^4}{1+x^8} \, dx$$ The answer at the back of the book is $$\frac{\pi}{4\sin(\frac{3\pi}{8})}$$
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### Complex number contour integral

Determine the contour integral ∫Ѱ 1/z dx, where Ѱ is the positively oriented unit circle with centre at -2 given that Ѱ(t) = -2 + e^(it), 0<=t<=2pii. I understand that Ѱ is the positively ...
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### Calculate the $\int_0^{2\pi}\cos(mx)\cos(nx)dx$
I'm having trouble with this problem: Consider the integral: $$\tag 1\int_0^{2\pi}\cos(mx)\cos(nx)dx$$ a. Write $\cos(mx)$ and $\cos(nx)$ in terms of complex exponentials and compute ...