{VERSION 2 3 "SGI IRIS UNIX" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE " " -1 256 "" 1 24 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading \+ 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 0 "" {MPLTEXT 0 21 0 "" }}{PARA 257 "" 0 "" {TEXT 256 15 "Calculus Lab 4\n" }{TEXT 257 21 "The definite Integral" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 53 "Consider the region under the graph of the function " }}{PARA 4 "" 0 "" {TEXT -1 57 "f:=x->x^2 over the interval x=1..3. Divide this inte rval " }}{PARA 4 "" 0 "" {TEXT -1 53 "into n subintervals of equal len gth. Approximate the " }}{PARA 4 "" 0 "" {TEXT -1 53 "area under the g raph by rectangles using the leftbox " }}{PARA 4 "" 0 "" {TEXT -1 48 " and rightbox commands from the student package. " }}{PARA 4 "" 0 "" {TEXT -1 57 "The student package is a collection of routines designed \+ " }}{PARA 4 "" 0 "" {TEXT -1 55 "to carry out step-by-step solutions t o problems. It is " }}{PARA 4 "" 0 "" {TEXT -1 95 "loaded by the comma nd with(student). \nThe routines contained in the package are the foll owing:\n" }}{PARA 4 "" 0 "" {TEXT 258 402 "D Diff Doublei nt Int Limit \nLineint Point Product Sum \+ Tripleint \nchangevar combine completesquare distance equate \+ \nextrema integrand intercept intparts isolate \nleftbox le ftsum makeproc maximize middlebox \nmiddlesum midpoint minimi ze minimize powsubs \nrightbox rightsum showtangent simps on slope \ntrapezoid value \n" }{TEXT -1 18 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 222 "Calling sequence for functions:\nf:=x- >expression;\nCalling sequences for graphic display of n approximating rectangles: \nleftbox(f(x), x=a..b, n,);\nrightbox(f(x) , x=a..b,n, );\nHere is an example:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(plots):\nf:=x->1/(1+x^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(f(x),x=0..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "leftbox(f(x),x=0..1,10);" }}}{PARA 0 "" 0 "" {TEXT 259 190 "\nWhat is the difference between leftbox and \+ rightbox? Write the answer here:\n.................................... ...................................................................... ......." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 103 "Plot 12 approximatin g rectangles of the integral of\nf:=x->x^2 over the interval x=1..3. F irst define f." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 188 "Compute the area of the rectangl es. Let dx:=(b-a)/n;\nand area:=Sum(f(a+i*dx),i=1..n); then work out \+ the \nlimit of the Riemann sums by Limit(area,n=infinity);\nvalue(\"); \nHere is an example:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:= x->1/(1+x^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Area:=(a,b ,n)->Sum(f(a+i*(b-a)/n)*(b-a)/n,i=1..n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "area:=(a,b,n)->sum(f(a+i*(b-a)/n)*(b-a)/n,i=1..n):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalf(area(0,1,10)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "evalf(limit(area(0,1,n),n=in finity)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalf(int(f(x) ,x=0..1));" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 260 63 "What is \+ the difference between Sum and sum, and Area and area?\n" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 56 "Now do the same for f:=x->x^2; over the i nterval x=1..2." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 254 "Consider the region bounded by y =-x^2+5*x-2 and y=x.\nFind the volume of the solid obtained by revolvi ng this region about the x-axis. First plot the graphs, then find the \+ common intersections and finally, integrate.\nHere is an example for a nother choice:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "f:=x->-0.1 28*x^3+1.728*x^2-5.376*x+2.864:\ng:=x->0.08*x^3-0.84*x^2+1.44*x+4.32: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot([f,g],-1..10,color =[red,blue]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "rt:=fsolve (f(x)=g(x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "Int(g(x)- f(x),x=rt[1]..rt[2]) + Int(f(x)-g(x),x=rt[2]..rt[3]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "int(g(x)-f(x),x=rt[1]..rt[2]) + int (f(x)-g(x),x=rt[2]..rt[3]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 41 " Now do the same for y=-x^2+5*x-2 and y=x." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}}}{MARK "9 0 0" 30 }{VIEWOPTS 1 1 0 3 2 1804 }