Stable your plots and worksheet together. Due Fri 13 Nov

This project has 5 parts. All plots need your name as part of the title.
(The line integrals are 2D for this project.) Worksheet needs your name
and small fonts as usual.

Line integrals. Use maple to draw `plots like Figure 2 on page 897'
Eventually each line integral over a curve C reduces to integrating a
function like int(g(t),t=a..b). What we want is a `curtain' of height
g(t) over the curve C. If C is given by <x(t), y(t)>, t=a..b then
we want to plot the surface <x(t), y(t), s*g(t)> t=a..b, s=0..1.
We can do this with plot3d as follows
plot3d([x(t),y(t),s*g(t)],t=a..b,s=0..1,title=`line curtain`,axes=BOXED);

Here for example is problem 17 section 14.2 (page 906)
> P:=(x,y)->x^2*y;

                                              2
                               P := (x,y) -> x  y
--------------------------------------------------------------------------------
> Q:=(x,y)->-x*y;

                               Q := (x,y) -> - x y
--------------------------------------------------------------------------------
> x:=t->t^3; dx:=diff(x(t),t);

                                             3
                                  x := t -> t

                                            2
                                   dx := 3 t
--------------------------------------------------------------------------------
> y:=t->t^4; dy:=diff(y(t),t);

                                             4
                                  y := t -> t

                                            3
                                   dy := 4 t
--------------------------------------------------------------------------------
> g:=t->P(x(t),y(t))*dx+Q(x(t),y(t))*dy;

                  g := t -> P(x(t), y(t)) dx + Q(x(t), y(t)) dy
--------------------------------------------------------------------------------
> g(t);

                                     12      10
                                  3 t   - 4 t
--------------------------------------------------------------------------------
> plot3d([x(t),y(t),s*g(t)],t=0..1,s=0..1,axes=BOXED,scaling=CONSTRAINED,labels=[`x`,`y`,`z`]);
--------------------------------------------------------------------------------
> int(g(t),t=0..1);

                                         19
                                      - ---
                                        143
--------------------------------------------------------------------------------



For each part we need a plot and the maple answer to the line integral.
The parts are
1. 14.2 #3,
2. 14.3 #11
3. F=<y,x> around the circle r(t) = <cos(t),sin(t)> t=0..2Pi,
for the line integral F dot dr. 
4. F=grad f where f(x,y) = arctan (y/x) around the circle in 3.
Hint: your problem is caused by x, and y already being defined. Try
again after doing unassign('x','y');
5. 14.2 #7,