Math 2401 Final
Open Book and Notes. Carefully explain your proceedures and answers. Calculators allowed, but answers mush be exact.
Problem 1 (10 points)
Find the surface integral ààcurl F×nâ Σ, over the surface S,
which is given by z =x2+y2, 0 £z£2. Here F =Ix3y2M i+xy2 j+x z k .
Set this up as a surface integral and convert to an ordinarydouble
integral. Then use Stokes’ s Theorem to convert to line integral HsL. Convert
these line integral HsLto ordinary one variable integral HsL. The surface
S does not include the top of the cone. The normal is the one illustrated
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Problem 2 (9 points)
Find T and N for the curve x(t) = cos(t), y = sin(t), z =
t3
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Final Spring 2007 Tom Morley 8:00 am
Problem 3 (10 points)
Find the area of the cardiod r= (1-cos( Θ)) that is above the curve y = |x| (absolute value).
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Problem 4 (9 points)
Find the the box of minumum cost constructed WITHOUT TOP if the cardboard for the sides is 2 cents a square foot,, and the
cardboard for the bottom is 8 cents a square foot. The box is to have a total volume of 64 square feet.
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