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.

I am having trouble figuring out how to input the following functions:

1. Use Maple to find (vector)T for the vector function r=(cost+tsint)i+(sint-tcost)j+5k

2. Find the length of the curve, r=(3cost)i+(3sint)j