document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=362177>Question 362177</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation:<BR>\n" );
document.write( "Explain why the following integrals are improper and determine whether they are<BR>\n" );
document.write( "convergent or divergent. Evaluate those that are convergent.\r<BR>\n" );
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document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+int%28+xe%5E%28-3x%29%2C+dx%2C+0%2C+infinity+%29+ ALIGN=MIDDLE  ALT=\"+int%28+xe%5E%28-3x%29%2C+dx%2C+0%2C+infinity+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+int%28+1%2F+xln%5E2x%2C+dx%2C+pi%2C+infinity+%29+ ALIGN=MIDDLE  ALT=\"+int%28+1%2F+xln%5E2x%2C+dx%2C+pi%2C+infinity+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258123 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=258123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "These integrals are improper because you have to calculate them as a limit.  You cannot calculate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int_a^\infty\ f(x)dx\">\r<BR>\n" );
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document.write( "directly. You must calculate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \lim_{b\rightarrow\infty}\,\int_a^b\ f(x)dx\">\r<BR>\n" );
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document.write( "From a table of integrals:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \int\ xe^{cx}dx\ =\ \frac{e^{cx}}{c^2}\left(cx\ -\ 1\right)\">\r<BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\ =\ -3\"> and replace the upper limit with an arbitrary variable, say <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> and then take the limit as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> increases without bound.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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