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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/>

<a NAME="E1:47"/>
 <a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a>  <a href="fcont_1.html#R2" title="FCONT_1:pred.2">is_continuous_on</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="integra8.html#E46"><i><font color="Green" title="E44">Lm3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:47"/>
(  <a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a>  <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a>  <a href="rfunct_1.html#R3" title="RFUNCT_1:pred.3">is_bounded_on</a> <font color="Maroon" title="c1">A</font> )
 <b>by </b><i><a class="ref" href="integra5.html#T10" title="INTEGRA5:th.10">INTEGRA5:10</a>, <a class="ref" href="integra5.html#T11" title="INTEGRA5:th.11">INTEGRA5:11</a></i>;<br/>


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