Triple Integrals Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Compute the iterate integral

(2) Compute the iterate integral

(3) Compute the iterate integral

(4) Compute the iterate integral

(5) Compute the iterate integral

(6) Compute the iterate integral

(7) Compute the iterate integral

(8) Compute the iterate integral

(9) Compute the iterate integral

(10) Evaluate the triple integrals where is the boxed region  

(11) Evaluate the triple integrals where is the boxed region  

(12) Evaluate the triple integrals where is the region bounded by the paraboloid and the plane

(13) Evaluate the triple integrals where is the solid in the first octant bounded by the hemisphere and the coordinate planes.

(14) Find the volume of the solid bounded by the sphere and the paraboloid

(15) Find the volume of the solid of the region bounded by the cylinders and and the planes and

(16) Find the volume of the region between the two elliptic paraboloids and

(17) Change the order of integration to show that



Also, show that

(18) Higher-dimensional multiple integrals can be defined and evaluate in essentially the same way as double integrals and triple integrals. Evaluate the multiple integrals where is the four-dimensional "hyperbox" defined by and

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