document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395544>Question 395544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28+sin%282011%282x-3%29pi%29%2A%282x-3%29%5E2011%2C+dx%2C+-1%2C4%29 ALIGN=MIDDLE  ALT=\"int%28+sin%282011%282x-3%29pi%29%2A%282x-3%29%5E2011%2C+dx%2C+-1%2C4%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 #280705 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=280705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+2x+-+3 ALIGN=MIDDLE  ALT=\"u+=+2x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=du+=+2dx ALIGN=MIDDLE  ALT=\"du+=+2dx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We now have\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28sin%282011u%2Api%29%2Au%5E2011%29%2C+du%29 ALIGN=MIDDLE  ALT=\"int%28%28sin%282011u%2Api%29%2Au%5E2011%29%2C+du%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (I'm writing it at an indefinite integral for now. Don't forget the 1/2 at the end)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Letting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+u%5E2011 ALIGN=MIDDLE  ALT=\"y+=+u%5E2011\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dz+=+sin+%282011u%2Api%29+du ALIGN=MIDDLE  ALT=\"dz+=+sin+%282011u%2Api%29+du\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy+=+2011u%5E2010du ALIGN=MIDDLE  ALT=\"dy+=+2011u%5E2010du\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%281%2F%282011%2Api%29%29%2A%28-cos+%282011u%2Api%29%29 ALIGN=MIDDLE  ALT=\"z+=+%281%2F%282011%2Api%29%29%2A%28-cos+%282011u%2Api%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Applying integration by parts,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=int%28%28sin%282011u%2Api%29%2Au%5E2011%29%2C+du%29+=+%28u%5E2011%29%281%2F%282011%2Api%29%29%2A%28-cos%282011u%2Api%29%29+-+++int+%28+%28+%281%2F%282011%2Api%29%29%2A%28-cos%282011u%2Api%29%29%2A2011u%5E2010%29%2C+du%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Which is equal to:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E2011%29%281%2F%282011%2Api%29%29%2A%28-cos%282011u%2Api%29%29+-+%281%2Fpi%29int+%28%28-cos%282011u%2Api%29%2Au%5E2010%29%2C+du%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hopefully, by repeatedly using integration by parts, you should be able to get a sum of 2010 or 2011 terms that should be simplifiable in some way. However the easiest way is obviously to use the nint() function or the definite integral function on a graphing calculator.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );