Exam 16: Methods and Applications of Integration

Use the formula = - Ln + C to find )

Find the exact area of the region bounded by y = - 4x and the x-axis.Also sketch the region.

Find the exact area of the region bounded by the graphs of y = -x,y = 2x,y = 1,and y = 2.Also sketch the region.

Use Simpson's rule with n = 4 to estimate the value of

Solve the differential equation = .

Find the area of the region enclosed by the graphs of y = - and y = 2x.

The amount of a certain drug in a patient's body t days after it has been administered is C(t)= 6 units.Determine the average amount of the drug present in the patient's body for the first five days after the drug has been administered.

If = ,then y =

It is estimated that service industries will grow at the rate of R'(t)= 5 where t is the time in decades and R(t)is the percent of (non-farming)workers who are employed in the service industry.If 30 percent of the (non-farming)workers are now in the service industry,then use Simpson's rule and n = 4 to approximate 30 + the percentage of workers who are working in the service industry in 2 decades.

Find the area between the graph of y = f(x)= + + 3 and the x-axis on the interval .Use your graphing calculator to see a graph of this area.

Use the tables to find: dx

Find the average value of f(x)= 5 - over the interval .

Suppose that the population of a city in 1992 was 52,400 and in 1996 was 55,300.If the exponential law of growth is assumed,what is the expected population in 2007?

=

Find the exact area of the region bounded by the graphs of y = 9 - and y = 5 - 3x.Also sketch the region.

Health officials are studying the spread of a disease in a city of 50,000 people.At the beginning of the study,1000 people were infected.One week later,2000 people are infected.Assuming logistic growth,determine the number N of people that are infected t weeks after the beginning of the study.

Find the area of the region bounded by the given equations: y = - x - 9 and y = - + 3x + 7

=

The total amount of nuclear waste that will accumulate at a nuclear plant is given by Find

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression: