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A calculus problem involving the calculation of double integrals, finding the derivatives of a vector field, and transforming integrals to cylindrical and spherical coordinates.
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Math 241: Calculus I I I Name Test #
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(1) Calculate the following double integrals. (You may have to switch the order of inte- gration.)
(a)
0
y
y dx dy
(b)
0
0
sin dr d
(c)
0
py^ e
(x^3 ) (^) dx dy
(2) Let F = z i + x j + y k. Calculate the divergence and curl of F.
Divergence:
Curl:
(3) Calculate cylindrical co ordinates (r; ; z ) and spherical co ordinates (; ; ) for the p oint with rectangular co ordinates (x; y ; z ) = (
(r; ; z ):
(; ; ):
(6) Calculate
0
0
0
x^2 + y 2
dz dy dx:
