Evaluate the line integral in Stokes' Theorem to evaluate the surface integral ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper S (gradient times Bold Upper F )times Bold n dS. Assume that n points in an upward direction. Fequalsleft angle x plus y comma font size decreased by 6 y plus z comma font size decreased by 6 z plus x right angle; S is the tilted disk enclosed by r(t)equalsleft angle 4 cosine t comma font size decreased by 6 6 sine t comma font size decreased by 6 StartRoot 20 EndRoot cosine t right angle.

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the answer   is 200

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this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

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