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Consider the following. Mark the quantity on a copy of the graph of f. An area representing F(b) - F(a), where F' = f. The figure below shows the standard normal distribution from statistics, which is given by the following equation. f(x) = 1/ e-x2/2, Statistics books often contain tables such as the following (below right), which show the area under the curve from 0 to b for various values of b. Use the values given in the table and the symmetry of the curve about the y-axis to find the following. The average value of y = v(x) equals 3 for 1 x 3, and equals 15 for 3 x 12. What is the average value of v(x) for 1 x 12? Suppose f is continuous, positive, decreasing, and concave up on the interval [5, 15] and suppose f = F' for some function F. Compare each pair of quantities, then determine which sign , or = is appropriate. Hint: Making a sketch of f might be helpful. Left hand sum for f on [5,15] with n=6 Left hand sum for f on [5, 15] with n=9 f(x)dx F(15)-F(5) Average value of f over the interval[5,15] Average value of f over the interval [5, 11] A fungus is spread through a forest of trees. The rate at which new trees get the fungus is given in the table below. Using a left-hand Riemann sum with n = 4, estimate the total number of new trees getting the fungus in the first 8 months. Find an underestimate with n = 4 for the total number of new trees getting the fungus during the first 8 months. What are the units of your answers to parts (a) and (b)?

Explanation / Answer

1) Option A

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2)

a) 0.1359

b) 0.8185

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3) 141 / 11

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4)

a) >

b) =

c) <

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5)

a) 788

b) 788

c) trees

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