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.
