These are 2 problems

4. A sheet of corrugated roofing is constructed by pressing a flat sheet of aluminum into one whose cross section has the form of a sine wave. If the cross-section has a period of L in., and the thickness of the corrugated sheet is 24 in., the cross-section can be described by f(x) = 4 . sin (x) Suppose the manufacturer would like to produce corrugated panels that are 64 in. wide and 2 in. thick, with a period of 16 in. We saw on HW #2 that we would need a flat sheet of metal of length L = 1 + cos ? (x )dr to make a 64-in. corrugated panel. Use Simpson's Rule with Ar = 8 to estimate the length of this metal sheet. (Make sure to use radians!) 5. One of the most prominent applications of improper integrals is in the field of probability. The quantity of interest (for example, the height of an American adult) is called a random variable. The probability of it being within a certain range (for example, between 60 and 70 inches) is governed by a probability density function (f). The probability that this random variable (x = height) is within a certain range (a 6); that is, the probability that the random variable r is greater than 6