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Jun
27
comment A certain Complex line integral
I would trust your book in this case. Can you show what you have done? (be careful about the multi-valuedness of the logarithm function!)
Jun
24
comment How can I solve the integral below using complex variables?
Hint: $\sin x= \mathop{\rm Im} e^{ix}$...
Jun
14
comment Timesing by a negative switches the limits on an integral?
You know that $\int_a^b f(x) dx = F(b)- F(a)$. I guess you can take it from here...
Jun
8
comment How can I solve $\int \sqrt{x}^\sqrt{x}dx$
I doub't that Rellek's answer is correct (never trust CAS blindly)...
May
28
comment Prove that there is a real number $a$ such that $\frac{1}{3} \leq \{ a^n \} \leq \frac{2}{3}$ for all $n=1,2,3,…$
Implementing the algorithm on a computer leads to the result $\alpha \approx 5.62144865272$.
May
21
comment Integrate with $-d(x/y)$
What I am trying to say is that the line-integral does not depend on the path but only on the end-points. In fact it only depends on the ratio $y/x$ of the starting point and the end point.
May
21
comment Integrate with $-d(x/y)$
One question: wouldn't all these approaches in the end lead to the same result?
May
14
comment Circular solution of Kepler Problem
I'm sure this question is not self-contained. What is the Kepler problem? What is $a$ and $q$ and $t$?
May
14
comment How to do integration by parts with brownian motion?
Hint: Integration by parts originates from the product rule for derivates. Do you know how to determine $d( f_t g_t)$ for two stochastic processes $f_t$ and $g_t$?
May
14
comment How to do integration by parts with brownian motion?
Why do you know you want to perform integration by parts?
May
7
awarded  Popular Question
Apr
25
reviewed Close Velocity field arrows along null clines as well as outside null clines
Apr
25
reviewed Leave Open Find vector and parametric vector of a line
Feb
25
revised Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
edited body
Feb
25
comment Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
Regarding the sign: as you most probably well know the sign of the sqrt-operation is ambiguous as the function is multivalued in a complex setting. We need to take the branch which is analytically connected to $\sqrt{x^2 + wx}>0$ in the original integral when rotating the contour to the lower half plane.
Feb
25
comment Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
@glance: yes you need Re$(s)>0$ in the rotated integral. However, afterwards to can analytically continue the result to understand that it coincides with the original integral whenever the latter converges.
Feb
25
revised Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
edited body
Feb
25
comment Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
@glance: Sorry, that was a typo.
Feb
19
awarded  Yearling
Feb
10
comment Prove that $\sin x<x$, if $x>0$
I would believe that already for $x>1$ the inequality is obvious.