Math& 254
Problem Set 24
Triple Integrals in Cylindrical Coordinates
>f X
Objectives:
•
•
Set up and calculate iterated triple int egra ls in cylindrical coordinates.
Use triple integrals to calculate physical quantities such as mass, center of mass, and average
value.
Problem 01: Let E be the region enclosed by the paraboloid
5, and the xy-pla ne. Let f (x, y, z) = e 2 •
z = 1 + x 2 + y 2 , the cylinder x 2 + y 2
2..= 1+ri
a)
Set up an integral of f(x,y ,z) over E in cyli ndrical coordinates.
b)
Evaluate the integral.
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