document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=556723>Question 556723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the volumes of the solids generated by revolving the regions bounded by the lines and curves :<BR>\n" );
document.write( "y=x^3 (x cube)<BR>\n" );
document.write( "y=0<BR>\n" );
document.write( "x=2 \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362220 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, draw the graph of the function and the rotation. You didn't specify which axis you rotate the region about. I'll assume you rotate about the x-axis.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We want to evaluate the integral\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \int_{0}^{2} \pi (x^3)^2 \, dx = \pi \int_{0}^{2} x^6 \, dx\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is equal to\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\pi x^7}{7}\"> evaluated at x = 2, minus the value at x = 0, or simply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{128 \pi}{7}\">. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );