Exam 16: Methods and Applications of Integration

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 the trapezoidal rule and to approximate 30 + the percentage of workers who will be working in the service industry in 2 decades.

Use the table below to determine dx.Indicate the formula number employed. I. + C II. + C III. + C IV. + C

Use the trapezoidal rule with n = 3 to estimate the value of

Use the formula ln + C to find .

A surveyor measured the length of a piece of land at 100-ft intervals (x),as shown in the table.Use Simpson's Rule to estimate the area of the piece of land in square feet.

Find the area of the region bounded by the curve y = f(x)= - x and the x-axis on the interval .Use your graphing calculator to see a graph of this area.

Systolic blood pressure is the blood pressure in a body when the heart contracts.An animal undergoing laboratory testing was injected with an experimental drug.The animal's systolic blood pressure P (in millimeters of mercury)was found to be given by P = + 100; 0 ≤ t ≤ 4,where t was the number of hours after the injection.What was the average systolic blood pressure over the first two hours after the injection?

Either find the value of or show that it diverges.

Find the average value of the function f(x)= (x + over the interval .

Find the average value of the function f(x)= + 4 over the interval .

Use the trapezoidal rule with n = 3 to find an approximate value of

If = And y(-2)= - ,then

Use Simpson's rule with n = 4 to find an approximate value of

Use the tables to find:

Use the tables to find:

Use the tables to find:

The exact area of the region bounded by the graphs of y = + x + 1,x = -2,x = 1,and the x-axis is

Solve the differential equation: 4y' + 3 = 0,y(1)=

Find the average value of the function y = f(x)= + 3 on the interval .Use your graphing calculator to graph both y = f(x)= + 3 and y = on the same set of axes.Estimate the value of x when these two curves intersect.

The demand equation for a product is p = and the supply equation is p = 1 + q.Determine the consumers' surplus and the producers' surplus.