(*
CALCULUS 265 Honors
Fall Semester 2000
8:00 to 8:50 MTTF
Carver 0002

Instructor: Hentzel
Office: 432 Carver
Office Hours: 9:00-10:00 MTTF

E-mail  hentzel@iastate.edu
phone  294-8141
Website

http://www.math.iastate.edu/hentzel/honors.265 <##### NEW ADDRESS ####

Tuesday, September  12:  Section 13.3

p930:9
p931:11,16,19
p939:7
p940:9,19,20


A pile of sand is a cone with altitude six feet and radius of
base 6 feet.  Unfortunately it extends one foot across the lot line.
The neighbor complains, and the contractor agrees that the neighbor can
have the sand that is on the neighbor's property.  They come to you,
a college educated person.  Tell them how much sand should belong
to the neighbor.  

Use Mathematica to evaluate the volume in four ways.

*)


f[x_,y_] := 6 - Sqrt[x^2 + y^2];

(*  Integrate  dy dx *)
(*  Integrate  dx dy *)
(*  Integrate  dr dt *)
(*  Integrate  dt dr *)

(* Which of the four is this ? *)
h = Integrate[ f[r Cos[t], r Sin[t]] r,{r,5 Sec[t],6}]

Integrate[h,{t,-ArcCos[5/6],+ArcCos[5/6]}];

(* Which of the four is this ? *)
h = Integrate[ f[r Cos[t], r Sin[t]] r,{t,-ArcCos[5/r],+ArcCos[5/r]}];

Integrate[h,{r,5,6}];


(* Which of the four is this ? *)

h = Integrate[f[x,y],{x,-Sqrt[36-y^2],+Sqrt[36-y^2]}];

Integrate[h,{y,5,6}]


(* Which of the four is this ? *)

h = Integrate[f[x,y],{y,5,Sqrt[36-x^2]}];

Integrate[h,{x,-Sqrt[36-5^2],+Sqrt[36-5^2]}];