Question: I am in desperate need of assisstance in solving these problems. Help?

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.


4. a)graph the solid encolsed by the cone, z=√(x^2+y^2), and the planes, z=1, and z=2.

b)write the integral which finds the volume of this solid and avaluate it. Use spherical coordinates.


I cannot figure any of these out to save my life. Please help.

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