## How can Integrate of conjugate transpose in mathematica?

0 ConjugateTranspose[u[x,t]] (u_x)[x,t]+I vx,t[x,t] 0 -ConjugateTranspose[u[x,t]] (u^(1,0))[x,t]-I vx,t[x,t] 0 0
0 0 0

u_x and v_x denote the diferentiate with respect to x.I dont know how can integrate the complex conjugate with mathematica. Thanks a lot.

## Can I integrate an exiting blog platform into my website

I am working on an e-commerce website, which is developed in ASP.NET MVC… I want to build a blog for the website and add some content to the blog to improve website’s ranking in the Search result.

I want my blog to be reached using: my-site.com/blog

Is it possible to integrate an existing blog platform such as Medium or Blogger into my website?

## How to integrate Firebase to Libgdx?

I have an android game built with libgdx and what I’d like to do is to add some kind of authentication so I can connect the game with user data to firebase database.

I have some experience with firebase using it in native android apps, but I have no idea on how to connect "native code" with libgdx.

Researching I found these third party libs https://github.com/mk-5/gdx-fireapp/tree/master/gdx-fireapp-core and https://github.com/TomGrill/gdx-firebase

But as it does not provide any example it didn’t help me much.

So what’s the best way to "mix" native android code and libgdx? I want to be able to achieve things like storing data on db, implementing in-app-purchases, authenticating users. If I’m looking the wrong way please let me know too.

## How do I integrate vanilla Javascript to a wordpress website?

I am new to WordPress but I have been learning to code since February. I am helping a friend add a responsive slider to her WordPress website. I created this slider using HTML, CSS and JS and it works perfectly. However, I am having problems integrating them into WordPress.

The JS code is

const prev = document.querySelector('.prev'); const next = document.querySelector('.next'); const track = document.querySelector('.track'); const carouselWidth = document.querySelector('.carousel-container').offsetWidth; let index = 0; let initialPosition = null; let moving = false; let transform = 0; next.addEventListener('click', ()=>{   index++;   prev.classList.add('show');   track.style.transform = translateX(-${index * carouselWidth}px); if (track.offsetWidth - (index * carouselWidth) < carouselWidth) { next.classList.add('hide'); } }); prev.addEventListener('click', ()=>{ index--; next.classList.remove('hide'); if (index === 0) { prev.classList.remove('show'); } track.style.transform = translateX(-$  {0}px) })    const gestureStart = (e) => {   initialPosition = e.pageX;   moving = true;   const transformMatrix = window.getComputedStyle(track).getPropertyValue('transform');   if (transformMatrix !== 'none') {     transform = parseInt(transformMatrix.split(',')[4].trim());   } }  const gestureMove = (e) => {   if (moving) {     const currentPosition = e.pageX;     const diff = currentPosition - initialPosition;     track.style.transform = translateX(\$  {transform + diff}px);     } };  const gestureEnd = (e) => {   moving = false; }  if (window.PointerEvent) {   window.addEventListener('pointerdown', gestureStart);    window.addEventListener('pointermove', gestureMove);    window.addEventListener('pointerup', gestureEnd);   } else {   window.addEventListener('touchdown', gestureStart);    window.addEventListener('touchmove', gestureMove);    window.addEventListener('touchup', gestureEnd);        window.addEventListener('mousedown', gestureStart);    window.addEventListener('mousemove', gestureMove);    window.addEventListener('mouseup', gestureEnd);   }  

This is the code I added to the functions.php file. It adds all the CSS styles correctly.

function responsive_header(){         wp_enqueue_style( 'responsive_header_css', get_template_directory_uri() .'/css/responsiveslider.css' , array() );         wp_enqueue_script('responsive_header', get_stylesheet_directory_uri() . '/js/responsiveslider.js', array(), '',  false);          }     add_action('wp_enqueue_scripts', 'responsive_header'); 

What is weird is that if I add a hello world alert to my script it works but nothing else works. Am i doing this wrong or must I use jquery. I dont know jquery but I can learn it to implement this.

## How to derive and integrate this interpolation function?

I have a problem with this function that I interpolated with a discrete data, I need to derive and then integrate to have a numerical values.

perfil = Import[data,"Table"]     Extrados = Table[perfil[[x]], {x, 1, 26}]; Intrados = Table[perfil[[x]], {x, 26, 51}]; \[Eta]u = Interpolation[Extrados]; \[Eta]i = Interpolation[Intrados]; \[Eta]c = 1/2 (\[Eta]u[x] + \[Eta]i[x]); d\[Eta]c = D[\[Eta]c, x] 

But I have the following output: https://imgur.com/g8URnVF So I can’t have a numerical values. I need to derive it and then integrate it

Subscript[B, 0] = 2/\[Pi] \!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$\[Pi]$$]$$d\[Eta]c \ \[DifferentialD]\[Theta]$$\) 

But the solution it’s the same. Someone know another solution about this? Why mathematica doesn’t gave me a symbolic function?

## it says, N Integrate has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,20}

when I run the code it says,NIntegrate has evaluated to non-numerical values for all sampling points in the
region with boundaries {{0,20}

\[Chi][b_] := (Z/k1)*NIntegrate[Subscript[f, pp1][q]*Subscript[F, pp1][q]*BesselJ[0, q*b]*q, {q, 0, b}] +  (Nn/K1)*NIntegrate[Subscript[f, pn1][q]*Subscript[F, pn1][q]*BesselJ[0, q*b]*q, {q, 0, b}]   data = Table[{b, \[Chi][b]}, {b, 0, 5.1, 0.1}]   

## Integrate autocorrect grammar APIs into SER

Hello @sven,

I am wondering if you could add autocorrection API’s (for articles/text) into SER.

With Google increasing their ability to find spun text, it would this would be of great importance and benefit to all SER users. Especially those using spun text. In my own experience, I’ve manually taken some spun articles, used Grammarly on them, and seen some pretty convincing rank improvements. However, this method is manual, when I’m pretty sure the same thing can be accomplished automatically (but sadly, not by Grammarly, they don’t offer an API).

I found this one when searching around, there seems to be an autocorrection script already written, perhaps it could just be added to SER?

https://www.grammarbot.io/tutorial-automated-correction

Then a section in options for “autocorrection APIs” similar to have captchas are done? Over time, with the system being in place, more API’s could be added (and you could also gain affiliate commissions from any sites that offer them – I bet many SEO’s who use SER would sign up with these sites).

There are also other API’s as such perfecttense.com, but I haven’t really been able to figure out how to get an API key from them. Grammarbot as mentioned above seem to have already given us code to use for autocorrection, and would likely be the easiest to integrate.

This would be a massive time saver for all of us, I can’t overstate the magnitude of it and would be happy to make a donation to make this happen.

Let me know what you think.
Thanks!

## Question with Integrate and Region

Let’s say I’ve got a 2D region r=Region[Polygon[{{0,0},{1,0},{1,1}}]]. I can do integrals like Integrate[1,{x,y}\[Element]r], or Integrate[y,{x,y}\[Element]r], to calculate areas and area moments.

I’d like to do an integral like Integrate[c^2,{x}\[Element]r], where c is the height (ymax-ymin) of the region at a particular value of x.

Any ideas appreciated.

-David

## Solve Improper Integrate using Residue theorem for this integral [migrated]

I am trying to solve this integral

$$\int_{-\infty}^\infty \frac{x\cdot sin(x)}{x^2+4} \cdot dx$$

I have applied the residue theorem on a semicircle of radius $$R> 2$$, $$\gamma$$, so I have

$$\int_\gamma \frac{z\cdot sin(z)}{z^2+4} \cdot dz = \int_{-R}^R \frac{x\cdot sin(x)}{x^2+4} \cdot dx+ \int_{C_R} \frac{z\cdot sin(z)}{z^2+4} \cdot dz$$

where $$C_R = \{ z : z=R e^{i \theta} , \theta \in (0,\pi)\}$$, but I cannot limit the second integral to eliminate this contribution when $$R \to \infty$$ and I don’t know how I could do the integral in another way