restart;with(Maplets[Elements]):with(Maplets[Tools]):with(student):randomize():lightorange:="#FFB300":great:=[" Bullseye."," Right on the mark."," Great."," That's absolutely right."," Awesome. You're unstoppable."," Correct."," WOW, nailed that one."," You got it!"," YES! Right on."," Way to go."," Don't stop now."," I knew you could do it!"," Perfect. You're unstoppable."," Radical Dude."," Power house."," Sweet! Keep on Rockin'."," You rock!"," You got those mad skills."," Awesome!"," Wowzers! That was great!"," Awesome man!"," Good job! You really know what you are doing."," You're awesome kid."," Tearing it up."," Right on the money."," High Five!!!!!"," Cool Beans."," What a nerd!"," You're so money."," You're a genious."," You hit the nail on the head."," Excellent!"," If I had a cookie, I'd give it to you."," You're a winner."," That's a winner."," Whoop! Way to go."," That's the way, ah ha ah ha, I like it."," Oh yeah!"," You're the bomb!"," That was fantastic!"," Oh Snap!",
" Would you like a cookie?",
" Would you like a medal?",
" Just keep on going and i will get you soon enough",
" You try way too hard",
" That one was easy. Try the next one",NULL]:sorry:=[" Sorry, that's not right."," Nope, but don't give up."," Not quite, it's a little off.",
"DANGER DANGER CALCULUS ERROR!!!!",
"DANGER DANGER CALCULUS ERROR!!!!",
"DANGER DANGER CALCULUS ERROR!!!!",
"DANGER DANGER CALCULUS ERROR!!!!",
"DANGER DANGER CALCULUS ERROR!!!!"," Bummer, thought you would get it this time."," Close, but no cigar."," Slightly off."," If you need help, please ask a human."," I don't know where you went wrong."," Sorry, killer problem."," No, but don't blow it off."," D'oh!"," That's whack."," Yikes! Really close. You'll get it next time."," Thought you would get it this time."," Nice try, but your answer is wrong."," Ask your neighbor for help."," Brutal kid."," That won't fly."," So close and yet so far."," So, that was just practice."," Ooooh...close."," A swing and a miss."," Better luck next time."," Oops."," Tilt. Play again."," I know you can do better."," Sorry Charlie."," Tisk, tisk. It's a tough one."," It takes a lot of wrongs to make a right."," Even Einstein didn't get everything right."," Oh man, you were so close."," Today's not your lucky day."," Don't quit your day job.",
"...Owned...",
"...Dominated...",
"...Served..."," You're colder than a polar bear's toenail.",NULL]:showgeneric:=[" OK That's just practice. But try doing it yourself."," That's fine for practice. Try doing it yourself."," Think about it and enter an answer yourself."," Next time, compute an answer yourself."," So that was practice. Try doing it yourself.",NULL]:showhint:=[" Next time, try the hints."," Read the hints and enter an answer yourself.",NULL]:showhelp:=[" Next time, read the Help menu."," Read the Help and enter an answer yourself.",NULL]:shows:=[ #Keep what is appropriate.op(showgeneric),op(showhint),#op(showhelp),#op(showlocal),NULL]:randgreat:=rand(1..nops(great)):randsorry:=rand(1..nops(sorry)):randshow:=rand(1..nops(shows)):otherfunction:=[
sin(x),
cos(x),
exp(x),
exp(-x),
sin(2*x),
cos(2*x),
exp(2*x),
exp(-2*x),
sin(3*x),
cos(3*x),
exp(3*x),
exp(-3*x),
sin(4*x),
cos(4*x),
exp(4*x),
exp(-4*x),
sin(x/2),
cos(x/2),
exp(x/2),
exp(-x/2),
sin(x/3),
cos(x/3),
exp(x/3),
exp(-x/3),
sin(x/4),
cos(x/4),
exp(x/4),
exp(-x/4),
NULL
]:randotherfunction:=rand(1..nops(otherfunction)):newfunction:=proc()
global Poly, Other;
Poly:=randpoly(x, degree=4, coeffs=rand(-5..5), terms=2);
#add square of poly of degree 2
Other:=otherfunction[randotherfunction()];
Set(MMLintegral(value)=("I"=Int(Poly*Other,x)));
Set(TFu=Poly);
Set(TFu1="");
Set(TFu2="");
Set(TFu3="");
Set(TFu4="");
Set(TFu5="");
Set(TFdv=Other);
Set(TFdv1="");
Set(TFdv2="");
Set(TFdv3="");
Set(TFdv4="");
Set(TFdv5="");
Set(TFintfinal=" ");
Set(reply1="", reply1(background)=white);
Set(reply2="", reply2(background)=white);
Set(reply3="", reply3(background)=white);
Set(reply4="", reply4(background)=white);
Set(reply5="", reply5(background)=white);
Set(reply6="", reply6(background)=white);
Set(replyall=" ", replyall(background)=white);
end proc:check1:=proc()
global Poly, Other;
local useru1 , userdv1, a, b;
useru1:=Get(TFu1::anything):
userdv1:=Get(TFdv1::anything):
a:=diff(Poly,x):
b:=int(Other,x):
if useru1=a and userdv1=b then
Set(reply1="good job", reply1(background)=green),
Set(replyall=great[randgreat()], replyall(background)=green);
else
Set(reply1="try again", reply1(background)=red),
Set(replyall=sorry[randsorry()], replyall(background)=red);
end if;
end proc: check2:=proc()
global Poly, Other;
local useru2, userdv2, a, b;
useru2:=Get(TFu2::anything):
userdv2:=Get(TFdv2::anything):
a:=diff(Poly,x,x):
b:=int(int(Other,x),x):
if useru2=a and userdv2=b then
Set(reply2="good job", reply2(background)=green),
Set(replyall=great[randgreat()], replyall(background)=green);
else
Set(reply2="try again", reply2(background)=red),
Set(replyall=sorry[randsorry()], replyall(background)=red);
end if;
end proc:check3:=proc()
global Poly, Other;
local useru3, userdv3, a, b;
useru3:=Get(TFu3::anything):
userdv3:=Get(TFdv3::anything):
a:=diff(Poly,x,x,x):
b:=int(int(int(Other,x),x),x):
if useru3=a and userdv3=b then
Set(reply3="good job", reply3(background)=green),
Set(replyall=great[randgreat()], replyall(background)=green);
else
Set(reply3="try again", reply3(background)=red),
Set(replyall=sorry[randsorry()], replyall(background)=red);
end if;
end proc:check4:=proc()
global Poly, Other;
local useru4, userdv4, a, b;
useru4:=Get(TFu4::anything):
userdv4:=Get(TFdv4::anything):
a:=diff(Poly,x,x,x,x):
b:=int(int(int(int(Other,x),x),x),x):
if useru4=a and userdv4=b then
Set(reply4="good job", reply4(background)=green),
Set(replyall=great[randgreat()], replyall(background)=green);
else
Set(reply4="try again", reply4(background)=red),
Set(replyall=sorry[randsorry()], replyall(background)=red) ;
end if;
end proc:check5:=proc()
global Poly, Other;
local useru5, userdv5, a,b;
useru5:=Get(TFu5::anything):
userdv5:=Get(TFdv5::anything):
a:=diff(Poly,x,x,x,x,x):
b:=int(int(int(int(int(Other,x),x),x),x),x):
if useru5=a and userdv5=b then
Set(reply5="good job", reply5(background)=green),
Set(replyall=great[randgreat()], replyall(background)=green);
else
Set(reply5="try again", reply5(background)=red),
Set(replyall=sorry[randsorry()], replyall(background)=red);
end if;
end proc:check6:=proc()
global Poly, Other;
local userint, a;
userint:=Get(TFintfinal::anything):
a:=int(Other*Poly,x):
if userint=a then
Set(reply6="good job", reply6(background)=green),
Set(replyall=great[randgreat()], replyall(background)=green);
else
Set(reply6="try again", reply6(background)=red),
Set(replyall=sorry[randsorry()], replyall(background)=red);
end if;
end proc: show1:=proc()
global Poly, Other;
local a, b:
a:=diff(Poly,x):
b:=int(Other,x):
Set(TFu1=a),
Set(TFdv1=b),
Set(reply1="weak...", reply1(background)=lightorange),
Set(replyall=shows[randshow()], replyall(background)=lightorange);
end proc:show2:=proc()
global Poly,Other;
local a, b:
a:=diff(Poly,x,x):
b:=int(int(Other,x),x):
Set(TFu2=a);
Set(TFdv2=b);
Set(reply2="weak...", reply2(background)=lightorange);
Set(replyall=shows[randshow()], replyall(background)=lightorange);
end proc:show3:=proc()
global Poly, Other;
local a, b:
a:=diff(Poly,x,x,x):
b:=int(int(int(Other,x),x),x):
Set(TFu3=a),
Set(TFdv3=b),
Set(reply3="weak...", reply3(background)=lightorange),
Set(replyall=shows[randshow()], replyall(background)=lightorange);
end proc:show4:=proc()
global Poly, Other;
local a, b:
a:=diff(Poly,x,x,x,x):
b:=int(int(int(int(Other,x),x),x),x):
Set(TFu4=a),
Set(TFdv4=b),
Set(reply4="weak...", reply4(background)=lightorange),
Set(replyall=shows[randshow()], replyall(background)=lightorange);
end proc:show5:=proc()
global Poly, Other;
local a, b:
a:=diff(Poly,x,x,x,x,x):
b:=int(int(int(int(int(Other,x),x),x),x),x):
Set(TFu5=a),
Set(TFdv5=b),
Set(reply5="weak...", reply5(background)=lightorange),
Set(replyall=shows[randshow()], replyall(background)=lightorange);
end proc:show6:=proc()
global Poly, Other;
local a:
a:=int(Poly*Other,x):
Set(TFintfinal=a),
Set(reply6="weak...", reply6(background)=lightorange),
Set(replyall=shows[randshow()], replyall(background)=lightorange);
end proc:TabInt:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN]('title'="Integration by Parts: The Tabular Method",
[ valign=none, inset=0, spacing=0,
[ halign=none,
Button("New Integral" , Evaluate('function'="newfunction"), background=magenta),
HorizontalGlue(),
Button("Quit", Shutdown(), background=pink)
],
[ border=true,
caption="Use Tabular Integration by Parts to compute the indefinite integral:",
MathMLViewer[MMLintegral](width=300,height=75),
HorizontalGlue()
],
[ halign=none,
"Table of u's and dv's. We get you started.",
HorizontalGlue()
],
[ halign=none,
"u =",
TextField[TFu](width=10, 'editable'=false, background=white),
"dv =",
TextField[TFdv](width=10, 'editable'=false, background=white),
" ",
Button("Hint" , RunWindow(Hint1), background=lightorange),
" ",
HorizontalGlue(),
" ",
HorizontalGlue()
],
[ halign=none,
"u1 =",
TextField[TFu1](width=10, background=turquoise),
"dv1 =",
TextField[TFdv1](width=10, background=turquoise) ,
HorizontalGlue(),
Button("Hint" , RunWindow(Hint2), background=lightorange) ,
Button("Check" , Evaluate('function'="check1"), background=green),
TextField[reply1]('width'=6, 'editable'='false', background=white) ,
Button("Show" , Evaluate('function'="show1"), background=lightorange)
],
[ halign=none,
"u2 =",
TextField[TFu2](width=10, background=turquoise),
"dv2 =",
TextField[TFdv2](width=10, background=turquoise),
HorizontalGlue(),
Button("Hint" , RunWindow(Hint2), background=lightorange) ,
Button("Check" , Evaluate('function'="check2"), background=green),
TextField[reply2]('width'=6, 'editable'='false', background=white) ,
Button("Show" , Evaluate('function'="show2"), background=lightorange)
],
[ halign=none,
"u3 =",
TextField[TFu3](width=10, background=turquoise),
"dv3 =",
TextField[TFdv3](width=10, background=turquoise) ,
HorizontalGlue(),
Button("Hint" , RunWindow(Hint2), background=lightorange) ,
Button("Check" , Evaluate('function'="check3"), background=green),
TextField[reply3]('width'=6, 'editable'='false', background=white) ,
Button("Show" , Evaluate('function'="show3"), background=lightorange)
],
[ halign=none,
"u4 =",
TextField[TFu4](width=10, background=turquoise),
"dv4 =",
TextField[TFdv4](width=10, background=turquoise) ,
HorizontalGlue(),
Button("Hint" , RunWindow(Hint2), background=lightorange) ,
Button("Check" , Evaluate('function'="check4"), background=green) ,
TextField[reply4]('width'=6, 'editable'='false', background=white),
Button("Show" , Evaluate('function'="show4"), background=lightorange)
],
[ halign=none,
"u5 =",
TextField[TFu5](width=10, background=turquoise),
"dv5 =",
TextField[TFdv5](width=10, background=turquoise),
HorizontalGlue(),
Button("Hint" , RunWindow(Hint2), background=lightorange) ,
Button("Check", Evaluate('function'="check5"), background=green),
TextField[reply5]('width'=6, 'editable'=false, background=white),
Button("Show", Evaluate('function'="show5"), background=lightorange)
],
[ halign=none, border=true,
caption="Integral",
"I =",
TextBox[TFintfinal](width=35, height=3),
HorizontalGlue(),
Button("Hint", RunWindow(Hint3), background=lightorange),
Button("Check" , Evaluate('function'="check6"), background=green),
TextField[reply6]('width'=6, 'editable'=false, background=white),
Button("Show" , Evaluate('function'="show6"), background=lightorange)
],
[ halign=none,
TextBox[replyall](width=60, height=2, 'editable'=false, background=white)
],
[ halign=none,
"Programmers: Philip T Segura, Owen Reese",
HorizontalGlue(),
"@ copyright Philip B. Yasskin 2007"
]
]),
Window[Hint1]('title'="Choosing u and dv Functions",
[ TextBox( width=60, height=12, editable=false, background=white, "
Choosing the two functions for Tabular Integration:\n
Tabular integration by parts only works if the nth
derivative of the u function goes to zero.
Therefore, the u function must be a polynomial.\n
The dv function can be any function of x.
However, tabular integration works best when the
dv function can be easily integrated multiple times,
such as sin(x), cos(x), e^x.
"),
Button("Close", CloseWindow(Hint1), background=pink)
]
),
Window[Hint2]('title'="Filling in the Table",
[ TextBox( width=65, height=14, editable=false, background=white, "
Fill in the table with values of u and dv.\n
The first column should contain increasing derivatives of u.
In particular, u1 is the first derivative of u,
u2 is the second derivative of u, etc.\n
The second column should contain increasing integrals of dv.
In particular, dv1 is the first antiderivative of dv,
dv2 is the second antiderivative of dv, etc.\n
Continue until the derivative of u goes to zero.
This may not require you to use all of the available rows.
"),
Button("Close", CloseWindow(Hint2), background=pink)
]
),
Window[Hint3]('title'="Computing the Integral",
[ TextBox( width=67, height=9, editable=false, background=white, "
To compute the integral of the function by the tabular method,
you multiply the u and dv table values in a particular order.
First multiply u * dv1. Then subtract u1 * dv2. Next add u2 * dv3.
Continue until the u value is 0.\n
In brief, your integral should have the form of:
u * dv1 - u1 * dv2 + u2 * dv3 - u3 * dv4 + u4 * dv5
"),
Button("Close", CloseWindow(Hint3), background=pink)
]
)
):Maplets[Display](TabInt);