C conman Member Joined May 2, 2005 Messages 139 Location West of Sydney Gender Male HSC 2007 Oct 9, 2006 #1 The velocity of a body P is given by Find the value of t when x=pi/4 if P starts from the origin.
P pLuvia Guest Oct 9, 2006 #2 dx/dt=cos2x/(1+sinxcosx) t=int.(1+sinxcosx)dx/cos2x =int.sec2x+tanx dx =tanx-ln(cosx)+C When t=0, x=0, C=0 t=tan-ln(cosx) When x=pi/4 t=1-ln(1/sqrt{2}) =1+1/2(ln2)
dx/dt=cos2x/(1+sinxcosx) t=int.(1+sinxcosx)dx/cos2x =int.sec2x+tanx dx =tanx-ln(cosx)+C When t=0, x=0, C=0 t=tan-ln(cosx) When x=pi/4 t=1-ln(1/sqrt{2}) =1+1/2(ln2)
