Exam 5: Accumulated Change: the Definite Integral

A large scale commercial bakery makes cream filling for snack cakes. The bakery puts a new machine into production. The machine ramps up gradually, increasing cream filling production at a rate of pounds per day over the first week. How many pounds of cream filling does the new machine make during the first week of production?

A new factory worker is put to work assembling gadgets. He is fairly slow at first, but over a period of days gets much faster. His employer constructs the following table to evaluate his progress over the first 20 days he is on the job. Give a n upper estimate for the number of gadgets the worker assembled the first 10 days on the job.

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 time at which the line disappears.

Given the following graph of f, which is the best approximation for ?

If the upper estimate of the area of a region bounded by the curve in the following figure, the horizontal axis, and the vertical lines x = 3 and x = -3 is 15, what is the upper estimate if the graph is shifted up 2 units?

A large ice cube is melting at a rate of cm³ per minute, where t is time in minutes. If is the volume of the ice cube at time t = 0 minutes, which one of the following expresses the volume of the ice cube after 4 hours?

A car is observed to have the following velocities at times t = 0, 2, 4, 6: Give a lower estimate for the number of feet the car traveled in first 6 seconds.

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

An air conditioning unit is switched on in an F room. The room is cooling off at a rate of degrees F per minute, with t in minutes after the unit was turned on. Set up an appropriate integral and evaluate it with a calculator to find the temperature of the room after 10 minutes. Round to the nearest degree.

You plan to approximate the definite integral by Riemann sums. Which Riemann sum will be larger, the right or the left?

What are the units of if t is measured in km/hr and f is in hours?

Use a calculator to evaluate . Round your answer to 2 decimal places.

Find the area included between the curves and , from x = 1 to x = 2. Round to 2 decimal places.

A stamp collector has 3000 stamps in his collection on January 1, 2005, and is collecting more stamps at a rate of stamps per week, where t is time in weeks since January 1, 2005. Which of the following expresses the number of stamps in his collection at the end of 2005?

Use an integral to find the area under the graph of for .

Consider a sports car which accelerates from 0 ft/sec to 85 ft/sec in 5 seconds (85 ft/sec = 58 mph). The car's velocity is given in the following table. Over which time interval in the average acceleration the smallest?

A shop is open from 9am-7pm. The function graphed below gives the rate at which customers arrive (in people/hour) at time t. Suppose that the salespeople can serve customers at a rate of 80 people per hour. A. People have to start waiting in line before being served at about _____ o'clock. B. The number of people in line when the line is the longest is about _____.

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 time a person who arrives at 7:00 has to stand in line.

On a recently discovered planetoid, acceleration due to gravity is 13 feet/ sec². While building a research habitat, a hammer is dropped from the top of a tower and hits the ground in 15 seconds. Because the hammer is dropped, its initial velocity is 0. Use a graph of the velocity function to determine the height of the tower.

The marginal cost function of producing a particular product is given by , where q is quantity. If the fixed costs are $3000, what is the total cost to produce 10 items?