Tagged Questions
-1
votes
2answers
66 views
How to integrate complex exponential??
Consider
$$\int^{\frac{1}{2}}_{-\frac{1}{2} } e^{i2\pi f} \,df = \int^{\frac{1}{2} }_{-\frac{1}{2} } \cos(2 \pi f)\, df$$
Why do we only look at the real part? What about the imaginary part ...
0
votes
1answer
76 views
How to do complex integration. E.g. $ \int_\frac{\pi}{2}^{\frac{\pi}{2} + i} \cos(2z) \; \mathrm{d}z $
For my homework assignment I've been given a number of complex integrals to solve. I've already asked for help on a specific example here, but I was somewhat dissatisfied with the answers. The answers ...
2
votes
1answer
217 views
Evaluating real integral using residue calculus: why different results?
I have to evaluate the real integral
$$
I = \int_0^{\infty} \frac{\log^2 x}{x^2+1}.
$$
using residue calculus.
Its value is $\pi^3/8$, as you can verify (for example) introducing the function
$$
...
2
votes
1answer
219 views
integral of complex logarithm
Consider the integral
$$I=\int_0^{2\pi}\log\left|re^{it}-a\right|\,dt$$
where $a$ is a complex number and $0<r<|a|$. We have
...
1
vote
1answer
148 views
line integral versus complex integral
Let $a\in \mathbb C, r>0$ and $\gamma_r=\partial D(0,r)$. I want to evaluate the following line integral
$$I=\int_{\gamma_r}\frac{1}{|z-a|^2}ds.$$
I'm looking for a complex function $g(z)$ such ...
