Arc_integral.svg

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->

<svg
   xmlns:dc="http://purl.org/dc/elements/1.1/"
   xmlns:cc="http://creativecommons.org/ns#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
   xmlns:svg="http://www.w3.org/2000/svg"
   xmlns="http://www.w3.org/2000/svg"
   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
   width="333.60843"
   height="249.42099"
   id="svg2"
   version="1.1"
   inkscape:version="0.48.0 r9654"
   sodipodi:docname="Arc_integral.pdf">
  <defs
     id="defs4">
    <marker
       inkscape:stockid="Arrow1Mstart"
       orient="auto"
       refY="0"
       refX="0"
       id="Arrow1Mstart"
       style="overflow:visible">
      <path
         id="path3805"
         d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
         style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;marker-start:none"
         transform="matrix(0.4,0,0,0.4,4,0)"
         inkscape:connector-curvature="0" />
    </marker>
    <marker
       inkscape:stockid="Arrow1Mend"
       orient="auto"
       refY="0"
       refX="0"
       id="Arrow1Mend"
       style="overflow:visible">
      <path
         id="path3808"
         d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
         style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;marker-start:none"
         transform="matrix(-0.4,0,0,-0.4,-4,0)"
         inkscape:connector-curvature="0" />
    </marker>
    <marker
       inkscape:stockid="Arrow1Lend"
       orient="auto"
       refY="0"
       refX="0"
       id="Arrow1Lend"
       style="overflow:visible">
      <path
         id="path3802"
         d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
         style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;marker-start:none"
         transform="matrix(-0.8,0,0,-0.8,-10,0)"
         inkscape:connector-curvature="0" />
    </marker>
  </defs>
  <sodipodi:namedview
     id="base"
     pagecolor="#ffffff"
     bordercolor="#666666"
     borderopacity="1.0"
     inkscape:pageopacity="0.0"
     inkscape:pageshadow="2"
     inkscape:zoom="2.8284271"
     inkscape:cx="205.48264"
     inkscape:cy="185.81686"
     inkscape:document-units="px"
     inkscape:current-layer="layer1"
     showgrid="false"
     inkscape:window-width="1049"
     inkscape:window-height="827"
     inkscape:window-x="297"
     inkscape:window-y="11"
     inkscape:window-maximized="0"
     fit-margin-top="0"
     fit-margin-left="0"
     fit-margin-right="0"
     fit-margin-bottom="0" />
  <metadata
     id="metadata7">
    <rdf:RDF>
      <cc:Work
         rdf:about="">
        <dc:format>image/svg+xml</dc:format>
        <dc:type
           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
        <dc:title></dc:title>
      </cc:Work>
    </rdf:RDF>
  </metadata>
  <g
     inkscape:label="Layer 1"
     inkscape:groupmode="layer"
     id="layer1"
     transform="translate(-71.444313,-370.32826)">
    <rect
       style="fill:#666666;fill-opacity:1;stroke:none"
       id="rect2985"
       width="86.903999"
       height="30"
       x="71.444313"
       y="493.22595" />
    <path
       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;marker-start:none;marker-end:url(#Arrow1Mend)"
       d="m 158.84831,545.38996 0,-113.85644"
       id="path2987"
       inkscape:connector-curvature="0" />
    <path
       sodipodi:type="arc"
       style="fill:none;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:1, 3;stroke-dashoffset:0"
       id="path2989"
       sodipodi:cx="206.07112"
       sodipodi:cy="502.8392"
       sodipodi:rx="155.05841"
       sodipodi:ry="155.05841"
       d="m 320.95458,398.70035 c 47.41092,52.30258 53.50967,130.02747 14.83669,189.08469 L 206.07112,502.8392 z"
       transform="matrix(1.3168309,0,0,1.3168309,-112.51251,-154.26425)"
       sodipodi:start="5.546805"
       sodipodi:end="6.8629549" />
    <path
       style="fill:none;stroke:#000000;stroke-width:0.84804362px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
       d="m 363.26841,493.24954 0,29.28082"
       id="path2991"
       inkscape:connector-curvature="0" />
    <path
       inkscape:connector-curvature="0"
       id="path2994"
       d="m 358.57143,464.17449 4.78,28.88802"
       style="fill:none;stroke:#000000;stroke-width:0.84804362px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
    <path
       inkscape:connector-curvature="0"
       id="path2996"
       d="m 346.05379,421.26264 16.42924,55.00462"
       style="fill:none;stroke:#000000;stroke-width:0.84799999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:0.84799999, 0.84799999;stroke-dashoffset:0;marker-start:url(#Arrow1Mstart);marker-end:none"
       sodipodi:nodetypes="cc" />
    <path
       inkscape:connector-curvature="0"
       id="path2998"
       d="m 350.11838,434.72505 8.30006,28.0798"
       style="fill:none;stroke:#000000;stroke-width:0.84804362px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
    <path
       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;stroke-dashoffset:0"
       d="m 159,508.86218 195.75,-58.25"
       id="path3768"
       inkscape:connector-curvature="0" />
    <path
       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;stroke-dashoffset:0;marker-end:url(#Arrow1Mend)"
       d="m 158.83386,508.95062 222.66614,0"
       id="path3770"
       inkscape:connector-curvature="0" />
    <path
       transform="matrix(0.59684411,0,0,0.59684411,35.980975,208.52333)"
       d="m 354.8069,459.0125 c 4.19338,14.23119 6.32263,28.99055 6.32263,43.8267"
       sodipodi:ry="155.05841"
       sodipodi:rx="155.05841"
       sodipodi:cy="502.8392"
       sodipodi:cx="206.07112"
       id="path3772"
       style="fill:none;stroke:#000000;stroke-width:1.34038353;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;stroke-dashoffset:0"
       sodipodi:type="arc"
       sodipodi:start="5.9966334"
       sodipodi:end="6.2831853"
       sodipodi:open="true" />
    <path
       inkscape:connector-curvature="0"
       id="path3778"
       d="M 159,498.86218 389.75179,442.20317"
       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:1, 1;stroke-dashoffset:0;marker-end:url(#Arrow1Mend)"
       sodipodi:nodetypes="cc" />
    <path
       inkscape:connector-curvature="0"
       id="path3780"
       d="m 158.83386,498.95062 222.66614,0"
       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:1, 1;stroke-dashoffset:0" />
    <path
       sodipodi:type="arc"
       style="fill:none;stroke:#000000;stroke-width:1.05627322;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:1.05627322, 1.05627322;stroke-dashoffset:0"
       id="path3782"
       sodipodi:cx="206.07112"
       sodipodi:cy="502.8392"
       sodipodi:rx="155.05841"
       sodipodi:ry="155.05841"
       d="m 356.77975,466.36976 c 2.88856,11.93686 4.34872,24.17464 4.34978,36.45603"
       transform="matrix(0.75737981,0,0,0.75737981,2.8992033,117.79969)"
       sodipodi:start="6.0457629"
       sodipodi:end="6.2830988"
       sodipodi:open="true" />
    <text
       xml:space="preserve"
       style="font-size:5.6561842px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       x="278.40094"
       y="487.25211"
       id="text3784"
       sodipodi:linespacing="125%"><tspan
         sodipodi:role="line"
         id="tspan3786"
         x="278.40094"
         y="487.25211">$\alpha'$</tspan></text>
    <text
       xml:space="preserve"
       style="font-size:6.0181365px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       x="251.88185"
       y="493.92471"
       id="text3788"
       sodipodi:linespacing="125%"><tspan
         sodipodi:role="line"
         id="tspan3790"
         x="251.88185"
         y="493.92471">$\alpha$</tspan></text>
    <text
       xml:space="preserve"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       x="354"
       y="442.36218"
       id="text3792"
       sodipodi:linespacing="125%"><tspan
         sodipodi:role="line"
         id="tspan3794"
         x="354"
         y="442.36218">$P'$</tspan></text>
    <text
       xml:space="preserve"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       x="385.5"
       y="438.30151"
       id="text4982"
       sodipodi:linespacing="125%"><tspan
         sodipodi:role="line"
         id="tspan4984"
         x="385.5"
         y="438.30151">$x'$</tspan></text>
    <text
       sodipodi:linespacing="125%"
       id="text4986"
       y="418.09442"
       x="349.47488"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       xml:space="preserve"><tspan
         y="418.09442"
         x="349.47488"
         id="tspan4988"
         sodipodi:role="line">$y'$</tspan></text>
    <text
       xml:space="preserve"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       x="381.5"
       y="519.36218"
       id="text4990"
       sodipodi:linespacing="125%"><tspan
         sodipodi:role="line"
         id="tspan4992"
         x="381.5"
         y="519.36218">$x$</tspan></text>
    <text
       sodipodi:linespacing="125%"
       id="text4994"
       y="474.86218"
       x="165"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       xml:space="preserve"><tspan
         y="474.86218"
         x="165"
         id="tspan4996"
         sodipodi:role="line">$y$</tspan></text>
    <text
       xml:space="preserve"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       x="302.5"
       y="520.36218"
       id="text5928"
       sodipodi:linespacing="125%"><tspan
         sodipodi:role="line"
         id="tspan5930"
         x="302.5"
         y="520.36218">$r$</tspan></text>
    <text
       sodipodi:linespacing="125%"
       id="text5932"
       y="478.36218"
       x="212.5"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       xml:space="preserve"><tspan
         y="478.36218"
         x="212.5"
         id="tspan5934"
         sodipodi:role="line">$r'$</tspan></text>
    <text
       sodipodi:linespacing="125%"
       id="text5936"
       y="489.86218"
       x="136.5"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       xml:space="preserve"><tspan
         y="489.86218"
         x="136.5"
         id="tspan5938"
         sodipodi:role="line">$P$</tspan></text>
    <path
       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:1, 1;stroke-dashoffset:0"
       d="m 354.75,450.61218 0,58.25"
       id="path5942"
       inkscape:connector-curvature="0" />
    <path
       inkscape:connector-curvature="0"
       id="path5944"
       d="m 354.93392,450.64708 -196.14158,0"
       style="fill:none;stroke:#000000;stroke-width:0.80000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:0.8, 0.8;stroke-dashoffset:0"
       sodipodi:nodetypes="cc" />
    <text
       sodipodi:linespacing="125%"
       id="text5946"
       y="523.6048"
       x="346.29288"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       xml:space="preserve"><tspan
         y="523.6048"
         x="346.29288"
         id="tspan5948"
         sodipodi:role="line">$P_x'$</tspan></text>
    <text
       xml:space="preserve"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       x="140.75735"
       y="449.09442"
       id="text5950"
       sodipodi:linespacing="125%"><tspan
         sodipodi:role="line"
         id="tspan5952"
         x="140.75735"
         y="449.09442">$P_y'$</tspan></text>
    <text
       xml:space="preserve"
       style="font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Times New Roman;-inkscape-font-specification:'Times New Roman,'"
       x="159.5"
       y="520.86218"
       id="text5954"
       sodipodi:linespacing="125%"><tspan
         sodipodi:role="line"
         id="tspan5956"
         x="159.5"
         y="520.86218">$O$</tspan></text>
  </g>
</svg>