Question: (a) Evaluate the integral 1/ sin ((32 + 32 + 2 2) 4 ) adv . R U- u where R is the region between

(a) Evaluate the integral 1/ sin ((32 + 32 + 2 2) 4 ) adv . R U- u where R is the region between the two spheres x2 + y2 + 22 = 1 and x2 + y? + 2? = 3. (b) Let D be the smaller cap cut from a solid ball of radius 2 units by a plane 1 unit from the center of the sphere. Express the volume of D as an iterated triple integral in (a) spherical, (b) cylindrical, and (c) rectangular coordinates. Then (d) find the volume by evaluating one of the three triple integrals

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