Double Integrals In Polar Coordinates 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) Sketch the region of integration and then evaluate the iterated integral in polar coordinates given  

(2)  Sketch the region of integration and then evaluate the iterated integral in polar coordinates given  

(3)  Sketch the region of integration and then evaluate the iterated integral in polar coordinates given  

(4)  Sketch the region of integration and then evaluate the iterated integral in polar coordinates given  

(5)  Sketch the region of integration and then evaluate the iterated integral in polar coordinates given  

(6) Given the curve sketch the enclosed region and then use an iterated integral to find the area of the region.

(7) Given the curve sketch the enclosed region and then use an iterated integral to find the area of the region.

(8) Given the curves and sketch the enclosed region and then use an iterated integral to find the area of the region.

(9) Given the curves and sketch the enclosed region and then use an iterated integral to find the area of the region.

(10) Use polar coordinates to evaluate the iterated integrals

(11) Use polar coordinates to evaluate the iterated integrals

(12) Use polar coordinates to evaluate the iterated integrals

(13) Evaluate the iterated integral by converting to polar coordinates.

(14) Evaluate the iterated integral by converting to polar coordinates.

(15) Evaluate the iterated integral by converting to polar coordinates.

(16) Evaluate the iterated integral by converting to polar coordinates.

(17) Evaluate the iterated integral by converting to polar coordinates.

(18) Evaluate the iterated integral by converting to polar coordinates.

(19) Find the volume of the solid region common to the cylinder and the ellipsoid

(20) Find the volume of the ice cream cone bounded by the hemisphere and the cone

(21) Find the volume of the solid region bounded above by the cone below by the plane and on both sides by the cylinder

(22) For a constant where the plane cuts off a "cap" from the hemisphere Use a double integral in polar coordinates to find the volume of the cap. For what values of is the volume of the cap half the volume of the hemisphere?

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