document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33106>Question 33106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2)what is the value of integration(t*sin(t) dt) from 0 to pi(22/7) by the trapezoidal rule? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19527 by </B><A HREF=/tutors/aboutme.mpl?userid=sarah_adam><B>sarah_adam(201)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sarah_adam><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=19527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know the formula for integration by parts as<BR>\n" );
document.write( "Int(uv) = uv - Int(vdu) over the given interval<BR>\n" );
document.write( "so here let u = t and let v= sint<BR>\n" );
document.write( "du= dt and dv = -cost + c<BR>\n" );
document.write( "now applying the formula we get<BR>\n" );
document.write( "Int(tsint) = (tsint) - Int(-cost +c) over the interval of 0 and pi/2<BR>\n" );
document.write( "now applying over the interval<BR>\n" );
document.write( "{(pi/2*sinpi/2)-0} - {(-cos pi/2 +c) - (-cos 0 +c)}<BR>\n" );
document.write( "sin pi/2 =  1 ,cos pi/2 = 0 and  cos 0 =1<BR>\n" );
document.write( "so the final answer is<BR>\n" );
document.write( "pi/2 - (0+c+1-c)<BR>\n" );
document.write( "pi/2 - 1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );