# math

## Coal gas is produced at a gasworks. Pollutants in the gas are removed by scrubbers, which become less and less efficient as time goes on. The following measurements, made at the start of each month, show the rate at which pollutants are escaping (in tons/month) in the gas:

Time (months)0123456Rate (tons/month)36915223038

A. Make an overestimate and an underestimate of the total quantity of pollutants that escape during the first month.
overestimate =

functionsequation editor tons
underestimate = functionsequation editor tons

B. Make an overestimate and an underestimate of the total quantity of pollutants that escape for the whole six months for which we have data.
overestimate =

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underestimate = functionsequation editor

Note:  You can earn partial credit on this problem.

## A population of cattle is increasing at a rate of 800+70????800+70t per year, where ????t is measured in years. By how much does the population increase between the 8th and the 13th years?

Total Increase =

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## Problem 3.

The following table gives 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).

194019501960197019801990????t01020304050????E7.48.912.618.62119.2

Estimate the integral: ∫500????(????)????????≈∫050f(t)dt≈

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Note: 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)

## Problem 4.

Estimate the area under the graph of ????(????)=????2+4????f(x)=x2+4x from ????=3x=3 to ????=9x=9 using the areas of 33 rectangles of equal width, with heights of the rectangles determined by the height of the curve at

(a) left endpoints

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(b) right endpoints

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Note:  You can earn partial credit on this problem.

## Problem 5.

Without using a calculator evaluate the definite integral.

∫62(7????2−9????+8)????????=∫26(7×2−9x+8)dx=

functionsequation editor .

## Problem 6

∫151????(????)????????−∫91????(????)????????=∫????????????(????)????????∫115f(x)dx−∫19f(x)dx=∫abf(x)dx

where ????=a=

functionsequation editor   and   ????=b= functionsequation editor .

Note:  You can earn partial credit on this problem.

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