document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045314>Question 1045314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A \"mountain\" is formed by revolving the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+e%5E%28-x%29 ALIGN=MIDDLE  ALT=\"y+=+e%5E%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, around the y-axis. Calculate the volume of this mountain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660728 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=660728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = e^(-x)<BR>\n" );
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document.write( "note that the y intercept is (0, 1) since e^(-0) = 1<BR>\n" );
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document.write( "The volume(v) of the mountain is pi * integration from 0 to 1 of {f(y)}^2 * dy<BR>\n" );
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document.write( "note that x = f(y) is the equation expressed in terms of y<BR>\n" );
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document.write( "y = e^(-x) then<BR>\n" );
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document.write( "x = ln (1/y)<BR>\n" );
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document.write( "pi * integral from 0 to 1 of {ln(1/y)}^2 dy<BR>\n" );
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document.write( "pi * integral from 0 to 1 ( y * (log^2(1/y) +2*log(1/y) + 2) )<BR>\n" );
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document.write( "we can just evaluate it for y = 1<BR>\n" );
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document.write( "note that the ln of 1 is 0<BR>\n" );
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document.write( "pi * ( 1 * (0) + 2*(0) +2) = pi * 2 = 6.2832 <BR>\n" );
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document.write( "V = 6.2832 units^3<BR>\n" );
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