Mathematics 134 – Intensive Calculus for Science 2 Quiz 6 – March 17, 2006

Your Name:

Do all work on this sheet (front and back if needed). You have 15 minutes. No calculators on this quiz. If you do the extra credit question, leave answer in exact form.

A) (10) A thin metal plate has the shape of the region sketched below. The density of the metal is δ(x) = e^{3x} kg/m^{2} at all points. Give the integral to compute its total mass (you do not need to compute the value).

Extra Credit (5) Evaluate your integral in part A.

B) (15) The times students need to complete a final exam are distributed according to the density function

p(t) = ct^{3}

for 0 ≤ t ≤ 3 hours, and 0 for all other t. What is the value of c? Write down the integral that could be used to compute the probability that a randomly selected student takes between 2.5 and 3 hours to complete the exam. (Again, it’s not necessary to compute the integral.)