@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr:-BLP2HLSP-6
  skos:prefLabel "calcul intégral"@fr, "integral calculus"@en ;
  a skos:Concept ;
  skos:narrower psr:-XDWH7HWS-9 .

psr: a skos:ConceptScheme .
psr:-DKRGCZ1S-Z
  skos:prefLabel "théorème de Green"@fr, "Green's theorem"@en ;
  a skos:Concept ;
  skos:related psr:-XDWH7HWS-9 .

psr:-XDWH7HWS-9
  skos:altLabel "path integral"@en, "curvilinear integral"@en, "curve integral"@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Line_integral>, <https://fr.wikipedia.org/wiki/Int%C3%A9grale_curviligne> ;
  skos:related psr:-DKRGCZ1S-Z ;
  skos:definition """In mathematics, a <b>line integral</b> is an integral where the function to be integrated is evaluated along a curve.  The terms <i>path integral</i>, <i>curve integral</i>, and <i>curvilinear integral</i> are also used; <i>contour integral</i> is used as well, although that is typically reserved for line integrals in the complex plane.
<br/>The function to be integrated may be a scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes the line integral from simpler integrals defined on intervals. Many simple formulae in physics, such as the definition of work as <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle W=\\\\mathbf {F} \\\\cdot \\\\mathbf {s} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>W</mi>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="bold">F</mi>
<br/>        </mrow>
<br/>        <mo>⋅<!-- ⋅ --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="bold">s</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle W=\\\\mathbf {F} \\\\cdot \\\\mathbf {s} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f62e7b41bc9ba33e6f1d9c7e36d77c48d41a2149" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:9.951ex; height:2.176ex;" alt="{\\\\displaystyle W=\\\\mathbf {F} \\\\cdot \\\\mathbf {s} }"></span>,</span> have natural continuous analogues in terms of line integrals, in this case <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\	extstyle W=\\\\int _{L}\\\\mathbf {F} (\\\\mathbf {s} )\\\\cdot d\\\\mathbf {s} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="false" scriptlevel="0">
<br/>        <mi>W</mi>
<br/>        <mo>=</mo>
<br/>        <msub>
<br/>          <mo>∫<!-- ∫ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>L</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="bold">F</mi>
<br/>        </mrow>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="bold">s</mi>
<br/>        </mrow>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mo>⋅<!-- ⋅ --></mo>
<br/>        <mi>d</mi>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="bold">s</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\	extstyle W=\\\\int _{L}\\\\mathbf {F} (\\\\mathbf {s} )\\\\cdot d\\\\mathbf {s} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adcc983069f7d70133cc2efadc0560f8de7a93f0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:16.868ex; height:3.176ex;" alt="{\\	extstyle W=\\\\int _{L}\\\\mathbf {F} (\\\\mathbf {s} )\\\\cdot d\\\\mathbf {s} }"></span>,</span> which computes the work done on an object moving through an electric or gravitational field <span class="texhtml"><b>F</b></span> along a path <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle L}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>L</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle L}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="L"></span>.</span> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Line_integral">https://en.wikipedia.org/wiki/Line_integral</a>)"""@en, """En géométrie différentielle, l'intégrale curviligne est une intégrale où la fonction à intégrer est évaluée sur une courbe Γ. Il y a deux types d'intégrales curvilignes, selon que la fonction est à valeurs réelles ou à valeurs dans les formes linéaires. Le second type (qui peut se reformuler en termes de circulation d'un champ de vecteurs) a comme cas particulier les intégrales que l'on considère en analyse complexe. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Int%C3%A9grale_curviligne">https://fr.wikipedia.org/wiki/Int%C3%A9grale_curviligne</a>)"""@fr ;
  skos:broader psr:-BLP2HLSP-6 ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:prefLabel "line integral"@en, "intégrale curviligne"@fr .