ITEMS INFO 1. Practice similar Use the following figure, which shows a graph of f(a) to find each of the indicated integrals. (Click on the graph for a larger version.) Note that the first area (with vertical, red shading) is 33 and the second (with oblique, black shading) is 3. A. So f(ac) dac = B. S. f(x) dx = C. S. f(x)dx = D. SC If(x) |dx =CITEMS INFO N Practice similar Use the graph of f(x) shown below to find the following integrals. (Click on the graph for a larger version.) A. S , f(x)dx = B. If the vertical red shaded area in the graph has area A, estimate: S", f(x) dx = (Your estimate may be written in terms of A.)110 1.0 -2ITE 3. Practice similar Find the average value of f(x) = 8x + 3 over [1, 6] average value =ITEMS INFO 4. Practice similar The following table gives the the approximate amount of emissions, E, of nitrogen oxides in millions of metric tons per year in the US. Let t be the number of years since 1940 and E = f(t). 1940 1950 1960 1970 1980 1990 + 0 10 20 30 40 50 E 7 9.8 12.8 18.7 20.4 19.1 Estimate the integral: So f(t) dt ~ Be sure that you know what the units of your answer are, and what its meaning is! (Original data from the Statistical Abstract of the US, 1992)ITEMS INFO 6. Practice similar The figure below to the left is a graph of f(x), and below to the right is g(x). 1.5 1.5 85 -815 -0.5 0.5 2 -0.5 0.5 2 -0.5 -0.5 f (ac) g(ac) (a) What is the average value of f(x) on 0