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May you please help me to sketch the region of 0 < x < 1 and 1-x < y < 1-x^2.

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  • 1
    Use tikz to draw the lines 1-x and 1-x^2 and look up fill between on the site
    – daleif
    Dec 23, 2021 at 14:02
  • 3
    Should the first range of integration, 0<y<1, maybe be stated more directly as 0<x<1?
    – Mico
    Dec 23, 2021 at 15:58
  • Looks like people severely misunderstood what you want. It would be better if you for example draw a sketch by hand of what you want.
    – user202729
    Dec 23, 2021 at 16:17
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    @Mico you are right. Sorry it was a typo on my question
    – user118746
    Dec 23, 2021 at 18:45

2 Answers 2

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Here is a short code with pstricks:

\documentclass[border=6pt, pstricks, svgnames]{standalone}
\usepackage{pst-plot}

\begin{document}

\begin{pspicture*}(-2.95,-2.95)(3,3)
\psset{arrowinset=0.15,showorigin=false, labelFontSize=\scriptstyle, linejoin=1}
\psaxes[linecolor=LightSteelBlue, ticksize=-2pt 2pt]{->}(0,0)(-2.95,-2.95)(3,3)[$x$,-120][$y$, -120]
\pscustom[fillstyle=solid, fillcolor=Lavender, linestyle=none, algebraic]{\psplot{0}{1}{1 - x^2}\psset{linecolor=Lavender}\closepath)}
\psline(-2,3)(3,-2) 
\psparabola{-}(-3,-8)(0,1)
\end{pspicture*}

\end{document}

enter image description here

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  • Thank you very much
    – user118746
    Dec 23, 2021 at 18:43
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    You're welcome. Always glad when I can help!
    – Bernard
    Dec 23, 2021 at 18:57
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Is it what You want?

enter image description here

\documentclass{article}

\begin{document} 

\newcommand{\Int}{\int\limits}

\begin{equation}
\Int_{0}^{1} \Int_{1-x}^{1-x^2}f(x,y) \,dx\,dy
\end{equation}

\end{document}
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  • Yes exacly! Thanks
    – user118746
    Dec 23, 2021 at 13:21
  • @user118746 if You find my answer useful mark it as helpful, please. Dec 23, 2021 at 13:40
  • You answer is useful, but I need sketching the region of double integral
    – user118746
    Dec 23, 2021 at 13:43
  • You mean plot a graph? Dec 23, 2021 at 14:01
  • 1
    @user118746 - Do you have some information about the properties of f(x,y) you wish to share?
    – Mico
    Dec 23, 2021 at 16:00

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