The following table gives the the approximate amount of emissions, E, of nitroge

Question

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). t 1940 1950 1960 1970 1980 1990 E 6.9 9.3 12.8 18.6 20.4 19.4 (a) Using left endpoints, estimate the integral: Integrate f(t)dt between the limits 0 and 50 Approximately equal to (b) Using right endpoints, estimate the integral: Integrate f(t)dt between the limits 0 and 50 Approximately equal to 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)

Explanation / Answer

using left point aproximation:-

integral of f(x)dx from limits a to b ? Ln = from i = 1 to n ? f(x(i)?1)?x

in our case answer is 6.9*10 + 9.3*10 +12.8*10 +18.6*10 +20.4*10 metric tons of nitrogen oxides.

i.e. 680 metric tons of nitrogen oxides.

using right point aproximation:-

integral of f(x)dx from limits a to b ? Rn = from i = 1 to n ? f(x(i))?x

in our case answer is

9.3*10 +12.8*10 +18.6*10 +20.4*10 + 19.4*10 metric tons of nitrogen oxides.

i.e. 805 metric tons of nitrogen oxides.

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