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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="integra1.html#V1" title="INTEGRA1:attr.1">closed-interval</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:75"/>
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 ;<br/>

<a NAME="E2:75"/><b>then </b><i><font color="Green" title="E59">A2</font></i>: 
(  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="integra8.html#T37" target="_self" title="INTEGRA8:th.37">Th45</a></i>;<br/>
 <a href="integra5.html#K2" title="INTEGRA5:func.2">integral</a> <a href="sin_cos2.html#K4" title="SIN_COS2:func.4">cosh</a> ,<font color="Maroon" title="c1">A</font> = 
<span class="p1">(<span class="default"><a href="sin_cos2.html#K1" title="SIN_COS2:func.1">sinh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> 1</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 0
<b>by </b><i><a class="ref" href="sin_cos2.html#T16" title="SIN_COS2:th.16">SIN_COS2:16</a>, <a class="txt" href="integra8.html#E2:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="integra8.html#T57" target="_self" title="INTEGRA8:th.57">Th64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K8" title="POWER:func.8">number_e</a>  <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> </span>)</span>
<b>by </b><i><a class="ref" href="integra8.html#T17" target="_self" title="INTEGRA8:th.17">Th19</a></i>
;<br/>
<b>hence </b><a NAME="E4:75"/>
 <a href="integra5.html#K2" title="INTEGRA5:func.2">integral</a> <a href="sin_cos2.html#K4" title="SIN_COS2:func.4">cosh</a> ,<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K8" title="POWER:func.8">number_e</a>  <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> </span>)</span>
 ;<br/>


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