document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127249>Question 127249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The answer that I have come up with is: (e -1).2:<BR>\n" );
document.write( "The problem is what are the exact evaluation of, (integral sign), &#61682;2xe^(x^2) dx over the intervals (0, 1).  I feel this is not correct, can you verify that for me please?\r<BR>\n" );
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document.write( "Also please, I have determined that In x is not the correct completion of the formula, (integral sign), &#61682;(1/x).  Is that correct, or should I do more research on this subject?  \r<BR>\n" );
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document.write( "Thank you all, for your God given talent that helps us less fortunate.  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93225 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+2xe%5E%28x%5E2%29%2C+dx%2C+0%2C+1+%29 ALIGN=MIDDLE  ALT=\"int%28+2xe%5E%28x%5E2%29%2C+dx%2C+0%2C+1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given integral\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%5E2 ALIGN=MIDDLE  ALT=\"u=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du=2xdx ALIGN=MIDDLE  ALT=\"du=2xdx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gets replaced with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xdx ALIGN=MIDDLE  ALT=\"2xdx\"   DISABLED_style= \"max-width:90%; height:auto;\" > (you have to group these together) gets replaced with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du ALIGN=MIDDLE  ALT=\"du\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Also, since the first endpoint is 0, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But we want this in terms of u. So just plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%5E2 ALIGN=MIDDLE  ALT=\"u=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=0 ALIGN=MIDDLE  ALT=\"u=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Do the same thing with the other endpoint to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=1 ALIGN=MIDDLE  ALT=\"u=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we now have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+e%5Eu%2C+du%2C+0%2C+1+%29 ALIGN=MIDDLE  ALT=\"int%28+e%5Eu%2C+du%2C+0%2C+1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we now have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Eu%2BC ALIGN=MIDDLE  ALT=\"e%5Eu%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the integral of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Eu ALIGN=MIDDLE  ALT=\"e%5Eu\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Eu ALIGN=MIDDLE  ALT=\"e%5Eu\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+e%5Eu%2C+du%29=e%5Eu%2BC ALIGN=MIDDLE  ALT=\"int%28+e%5Eu%2C+du%29=e%5Eu%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's evaluate the endpoints\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5E1%2BC%29-%28e%5E0%2BC%29 ALIGN=MIDDLE  ALT=\"%28e%5E1%2BC%29-%28e%5E0%2BC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the endpoints and subtract\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e-1 ALIGN=MIDDLE  ALT=\"e-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms and simplify\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+2xe%5E%28x%5E2%29%2C+dx%2C+0%2C+1+%29=e-1 ALIGN=MIDDLE  ALT=\"int%28+2xe%5E%28x%5E2%29%2C+dx%2C+0%2C+1+%29=e-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Are you trying to evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+1%2Fx%2C+dx%29 ALIGN=MIDDLE  ALT=\"int%28+1%2Fx%2C+dx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?\r<BR>\n" );
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document.write( "The integral of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29%2BC ALIGN=MIDDLE  ALT=\"ln%28x%29%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+1%2Fx%2C+dx%29=ln%28x%29%2BC ALIGN=MIDDLE  ALT=\"int%28+1%2Fx%2C+dx%29=ln%28x%29%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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