Tagged Questions
2
votes
2answers
36 views
Calculate the length of curve $f(x)=\arcsin(e^x)$, check solution, please.
As in the topic, my task is to calculate the length of $f(x)=\arcsin(e^x)$ between $-1, 0$. My solution: I use the the fact, that the length of $f(x)$ is equal to $\int_{a}^b\sqrt{1+(f'(x))^2}dx$ ...
0
votes
1answer
86 views
A hard limit with integral sign
$$\displaystyle\underset{m\to +\infty }{\mathop{\lim }}\,\left[ \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\int_{0}^{x}{{{\left( \underset{n\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{1}{n} ...
2
votes
1answer
68 views
Two questions on trigonommetric sums and integrals
Is it true that $\int_{0}^{\infty}\sin(mx)\sin(nx) \, dx = \delta (m-n) $ although using Euler formula I get a linear combination of $ \delta(m-n) $ and $ \delta (m+n)$?
What is the sum ...
