How do you graph the definite integral of 1/x from -1 to 1?

Question

I want to make a graph of the function 1/x with the area under the curve shaded, but I have absolutely no idea how to do that since the curve isn't continuous. Optimally, the negative area and positive area would be shaded with different colors. I would also like there to be a label that says f(x)=1/x. I made this image in Desmos to show an example of the image I'm trying to get:

Answer 1

You are a new contributor so it would be better if I direct you to a more professional tool than tkz-fct. My package is only useful for small graphs. I think pgfplots is what you need. I think you will get answers with this one.

To be complete with tkz-fct you need to install gnuplot. This is what does the calculations. Otherwise you can do what you need with just TikZ.

updated : with xstep different from 1 use x and not x

\documentclass{article}
\usepackage{tkz-fct}

\begin{document}
 \begin{tikzpicture}[scale=2]  
  \tkzInit[xmin=-4,xmax=4,ymin=-4,ymax=4,xstep=2,ystep=2]
  \tkzClip[space=1]
 \tkzGrid
  \tkzAxeXY
  \begin{scope}
    \tkzFct[color=blue, domain=0:4]{1./\x}
    \tkzFct[draw=none, domain=0:4]{0}
    \tkzDrawAreafg[color=blue!10,domain = 0.01:4]
  \end{scope}
  \begin{scope}
    \tkzFct[draw=none, domain=-4:0]{0}
    \tkzFct[color=red ,domain=-4:0]{1./\x}  
  \tkzDrawAreafg[color=red!20,domain = -4:-0.01]
   \end{scope}
\end{tikzpicture}
\end{document}

Complement :

You can mix tkz-fct and TikZ

\documentclass{article}
\usepackage{tkz-fct,mathtools}

\begin{document}
\begin{tikzpicture}[scale=3] 
\tkzInit[xmin=0,xmax=4,ymin=-1.5,ymax=1.5] 
 \tkzAxeX\tkzAxeY
\tkzDefPoint(1,0){x} 
\tkzDrawPoint[color=blue,size=0.6pt](x) 
\shade[top color=gray!80,bottom color=gray!20] (1,0)%
    plot[id=ln,domain=1:2.718] function{log(x)} |-(1,0); 
\draw[color=blue] plot[id=ln,domain=0.2:4,samples=200]function{log(x)};
\tkzText[draw,color= black,fill=brown!50](2,-1)%
    {$\mathcal{A} = \int_1^{\text{e}}\ln(x)\text{d}x =\big[x\ln(x)\big]_{1}^{\text{e}} = \text{e}$}
\tkzText[draw,color= black,fill=brown!50](2,0.3){$\mathcal{A}$}
 \end{tikzpicture}
\end{document}

Answer 2

Here is a plain Asymptote way that you can compile online. Plain things are suitable for beginners. Here is a link on overleaf. If you want to compile on desktops, make sure having Asymptote installed.

// copy http://asymptote.ualberta.ca/ and click Run
usepackage("amsmath");  // for \dfrac
import graph;
import math; // for grid
unitsize(1cm);
size(6cm);
real f(real x){return 1/x;}
int a=4;
add(shift(-a,-a)*scale(2)*grid(a,a,gray));

real s=.1;
path p=graph(f,s,a);
path q=graph(f,-a,-s);
pen penp=magenta, penq=deepcyan;
fill((0,0)--(0,a+1)--p--(a+1,0)--cycle,penp+white+opacity(.5));
fill((0,0)--(-a-1,0)--q--(0,-a-1)--cycle,penq+opacity(.5));
draw(p,penp+1pt);
draw(q,penq+1pt);

clip(box((a,a),(-a,-a)));

draw(Label("$x$",EndPoint,align=SW),(-a-1,0)--(a+1,0),Arrow(TeXHead));
draw(Label("$y$",EndPoint,align=SW),(0,-a-.5)--(0,a+1),Arrow(TeXHead));
label(Label("p.v. $\displaystyle\int_{-a}^a\dfrac{1}{x}\,dx=0$",FillDraw(yellow,black)),(-2,2));
label(Label("$a$",Fill(white)),(a,0),2S);
label(Label("$-a$",Fill(white)),(-a,0),2N);