\START85\
\COMMENT=Program file dated 03/14/00, 15:59
\NAME=APPROX
\FILE=C:\TI85LINK\PROGRAMS\APPROX.85P
:ClLCD
:Disp ""
:Disp "       Approx"
:Disp ""
:Disp "   by Nick Markham"
:Disp ""
:Disp "  markhamnr@aol.com"
:Pause 
:ClLCD
:InpSt "f(x): ",eqn
:\St>Eq\(eqn,y1):0\->\x
:Input "Lower: ",t
:Input "Upper: ",r
:Lbl A2
:If x==1:ClLCD
:Input "n: ",\LC-theta\
:While \LC-theta\\<=\3
:Disp "n must be \>=\ 4"
:Input "n: ",\LC-theta\
:End
:ClLCD
:2*sum seq(y1,x,t+(r-t)/\LC-theta\,r-(r-t)/(2*\LC-theta\),(r-t)/\LC-theta\\#\
)\->\y
:t\->\x:y1+y\->\y
:r\->\x:y1+y\->\y
:y*(r-t)/(2*\LC-theta\)\->\y
:Outpt(1,1,"f(x)=")
:Outpt(1,6,eqn)
:Outpt(2,1,"[         ,         ]"
:Outpt(2,2,t)
:Outpt(2,12,r)
:Outpt(3,1,"Trapezoid: ")
:Outpt(3,12,y)
:If mod(\LC-theta\,2)==0
:Then
:4sum seq(y1,x,t+(r-t)/\LC-theta\,r-(r-t)/\LC-theta\,2(r-t)/\LC-theta\)\#\
\->\y
:2sum seq(y1,x,t+2(r-t)/\LC-theta\,r-2(r-t)/\LC-theta\,2(r-t)/\LC-theta\\#\
)+y\->\y
:r\->\x:y1+y\->\y
:t\->\x:y1+y\->\y
:y*(r-t)/(3*\LC-theta\)\->\y
:Outpt(4,1,"Simpson's: ")
:Outpt(4,12,y)
:Else
:Outpt(4,1,"Simpson's: ----------"
:End
:Outpt(5,1,"Right    : ")
:Outpt(5,12,sum seq(y1,x,t+(r-t)/\LC-theta\,r+(r-t)/(2*\LC-theta\),(r-t\#\
)/\LC-theta\)*(r-t)/\LC-theta\)
:Outpt(6,1,"Midpoint : ")
:Outpt(6,12,sum seq(y1,x,t+(r-t)/(2*\LC-theta\),r-(r-t)/(4*\LC-theta\),\#\
(r-t)/\LC-theta\)*(r-t)/\LC-theta\)
:Outpt(7,1,"Left     : ")
:Outpt(7,12,sum seq(y1,x,t,r-(r-t)/(2*\LC-theta\),(r-t)/\LC-theta\)*(r-\#\
t)/\LC-theta\)
:Outpt(8,1,"Exact    :")
:Outpt(8,12,fnInt(y1,x,t,r)
:Pause 
:Lbl A4
:Menu(1,"Graph",A1,5,"Exit",A5,2,"n",A3)
:Lbl A3:1\->\x:Goto A2
:Lbl A1
:Shade(0,y1,t,r)
:Shade(y1,0,t,r)
:DispG:Goto A4
:Lbl A5
\STOP85\