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1. a)given ∫(0..4)∫(√x..2) of sin(pi)*y^3 dydx, graph the region, R, in the xy plane.

b)Write double integral which reverses the order of integration and then evaluate.


2. Find centroid of cardioid of region enclosed by cardioid r=1-sin(theta)


3. a)Graph wedge cut from cylinder x^2+y^2=9, and by planes, z=-y, and z=0, and above the xy plane.

b)Write the integral which finds the volume of the wedge and evaluate it.

Is the shortest distance to the centroid or the intersection?

Just a simple problem really.  I thought the centroid of a set (let's say 4 at this point) of points...

I had started to create a procedure for finding the centroid of a list of points.

Centroid := proc (list)
local a, centroid, x, y, i:
a := nops(list):
x := 0:
yi := 0:
for i from 1 to a do
x := x+list[i, 1]:
y := y+list[i, 2]:
end do:
print(`Centroid is at`,([xi, yi]/a)):
end proc:

But I thought there needs to be something simpler than that.  And here we are.

Centroid2 := proc (list)
local i:
print(`Centroid is at`, add(i, i = list...

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