# integral

1. ### Definite Integral involving Complete Elliptic Integral

Is anyone aware if there is an analytical solution to: ${\displaystyle \int_{a}^{b}} K(k)\; dk$ And: ${\displaystyle \int_{a}^{b}} E(k)\; dk$ where K and E are complete elliptic integrals of the first and second kind, with modulus k, and in both cases: 0â‰¤a<bâ‰¤1 I've found these in...
2. ### An integral

Hello all, Let \int_0^1 ((f(x))^2+2f(x)+3) dx where the derivatives of the function f^{(n)}(0)=1 \forall n\in \mathbb N.To prove that I<\frac{2891}{300}. All the best, Integrator
3. ### Integral

A function ............Please delete the topic. Thank you very much!
4. ### Evaluate integral

\int_{0}^{\infty} (e^{-x}+e^{-x^2 }+...+e^{-x^n })dx. To write it better : \int_{0}^{\infty} \sum_{i=1}^{n} e^{\displaystyle -x^i }dx
5. ### Integral convergence

For which values of s the integral converges ? \int_{0}^{\infty}e^{sx}\cos(sx)dx \; , s\in \mathbb{R}.
6. ### Cannot solve integral

Evaluate: \int_{0}^{1} \frac{x^{b}-x^{a}}{\ln(x)}dx\; . a\neq b, a,b>0.
7. ### Limit of postive function with bounded derivative and convergent improper integral

Is it true that for a continuous function X(t) where X(t)â‰¥0 and \int_{-\infty}^{-T}X(s)ds<\infty and X(t) is bounded together with its derivative: \lim \limits_{tâ†’âˆ’\infty} X(t)=0? If so, why?
8. ### Integral inequality

Compare e with : \int_{0}^{-\infty } e^{e^x } \cdot e^x dx .
9. ### Evaluate integral

I(n)=\underbrace{\int_{-\infty}^{\infty } \int_{-\infty }^{\infty} ...\int_{-\infty}^{\infty } }_{n}\prod_{j=1}^{n} x_{j}^{j} e^{-x_{1}^{2} -x_{2}^{2}-...-x_{n}^{2} } dx_{1} \cdot dx_{2}\cdot ...\cdot dx_n .
10. ### Understanding a specific Chebyshev integral

I have a situation where I'm trying to understand the physics of a cooling tower. Part of the solution for the model I'm working with involves an integral: C = \int_{T_{low}}^{T_{high}} \frac{1}{\left(h' - h_a\right)} dT where h' is a slowly varying, monotonically increasing function with...
11. ### Help with Calculus II Problem

Need help with this one. Can't seem to solve it. Thanks in advance
12. ### Evaluate integral

Evaluate I_{x}= \int_{1}^{x} \ln \ln(t) dt .
13. ### Help with this integral

$I=\displaystyle\int_~\frac{x^{1/3}}{\sqrt{1+x}}~dx$
14. ### Definite integral of box function

Evaluate integral if [ t + 1]^3 dt from t = 0 to t=x where [.] denotes the box function Please let me know how to proceed
15. ### double integral

Hello ,anyone got an idea about getting the area of the place surrounded by y=-x^2+x and y=-x by double integrals . really thanks by the way:D:D
16. ### Generalized Fourier Integral and Steepest descent path, Saddle point near the endpoin

I am looking forward to solving the integration in the following equation with the assumption that $ka$ is very large \begin{align} H = 2jka\int_{-\pi/2}^{\pi/2}\cos{(\varphi-\phi)}e^{jka[\cos{\varphi}+\cos{(\varphi-\phi)}]}\ d\varphi \end{align} I used the steepest descent path method to...
17. ### Evaluate integral

I(x,y,z)=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-x^{2} -y^{2} -z^{2} }dz\; dy \; dx .
18. ### How to solve this simple Laplace integral?

Check this Image. I tried to post it as an image but it takes the entire space of the post... It seems I have forgotten a lot about solving integrals... But I really need to remember quickly how to solve this kind of fractional integrals since I haven't memorized the Laplace "trick" formulas...
19. ### Integral

how to solve the integral with residues? If I can solve it like that
20. ### Solve integral

Help with the task please where L - is a segment connecting the points 0 and 1 + i