Exam 5: Accumulated Change: the Definite Integral

Use the following figure to find the value of

Sales of a new product are increasing at a rate of units per month, where t is time in months since the product was introduced. How many units were sold the first 3 months since the product was introduced? Set up an integral and use a calculator to evaluate it to the nearest whole unit.

Data for a function G is given in the following table. Estimate (to 3 decimal places). Average upper and lower sums.

If a function is concave up, then the left-hand Reimann sums are always less than the right-hand Reimann sums with the same subdivisions, over the same intervals.

A reagent is cooling in a laboratory instrument. Explain in words what means if is the temperature of the reagent in degrees Fahrenheit and t is time in minutes.

Use the following graph to estimate using the left Riemann sum with three terms.

Estimate the area above the curve and below y = 4 for . Round to 2 decimal places.

Below is a graph of the rate r in arrivals per minute at which students line up for breakfast. The first people arrive at 6:50 am and the line opens at 7:00 am. The line serves students at a constant rate of 20 students per minute. Estimate the length of the line at 7:10.

Find for .

Use the following figure to estimate (average left- and right-hand sums).

The Ethnic food line at the Cougar Eat can serve customers at the rate of about 30 per hour. From 10 am until 4 pm one day, the rate R at which customers entered then line was about customers per hour at t hours past 10 am. About how many customers were served between 10 am and 4 pm that day? Round to the nearest whole number.

In the following graph, does appear to be positive, negative, or zero?

The graph of is shown in the following figure. Given that , find .

A. Find a 4-term left Riemann sum approximation for the integral . Round to 1 decimal place. B. Is your answer in part (A) an underestimate or an overestimate?

Two cars start at the same time and travel in the same direction along a straight road. The following figure gives the velocity, v, of each car as a function of time, t. Which car reached the larger maximum velocity?

At time t, in seconds, the velocity v, in feet per second, of a car is given by for . A second car travels exactly 20 feet per second faster than the first car. How much greater will the left- and right-hand estimates for the distance traveled by the second car be that the left- and right-hand estimates for the distance traveled by the first car?

Data for a function G is given in the following table. Estimate .

Your rich eccentric friend has hired you to cover his back yard with grass and patio stone. If the southwest corner of his yard is taken as the origin, with the x-axis pointing eastward and distances measured in feet, then the boundaries of the yard are the lines x = 0, x = 100, y = 0, and f(x) = 110-0.5x. The border between grass and stone is , with grass covering all of the yard south of the curve. This border also bounds one side of the pool, the other side of the pool being surrounded by the curve . All of the rest of the yard is to be covered by stone. Estimate, to the nearest square yard, the area of the grass.

At time t, in seconds, your velocity, v, in meters per second, is given by for . Use to estimate how many meters you traveled during this time.

If is a production rate, measured in items per hour, then how many items were produced from hour 2 to hour 6?