Exam 15: Integration

Determine: dx

A marketing group is studying population trends.It predicts that the population P of a certain city will increase at the rate of people per year,where = and t is the number of years past 1980.What is the expected increase in population from 1980 to 2001?

Determine:

Determine:

=

Determine: dx

+ 2 dx =

Suppose the surface area of a 1.9 meter-tall person changes at the rate of = 0.14 square meters per kilogram,where x is the weight in kilograms.Find the decrease in surface area for a person whose weight decreases from 75 kilograms to 70 kilograms by evaluating

Determine: dx

An oil company estimates that for the next few months,oil will be pumped (in thousands of gallons per month)from a producing field at a rate of R(t)= + 9,where t is in months.Find dt.

If the rate of change of a company's revenue can be modeled by = 0.5t,then find r(t)the revenue function.

Suppose the rate of savings in a country is given by = 3.3 - 900 + 32,891.60,where t is the time in years,and S is the amount of money saved in billions of dollars.Find the function S(t)which gives the total amount of money saved.You may assume that $0 is saved at t = 0.

Determine: dz

After weeks of television promotion,an electronics store finds that its sales change at a rate given by where t is the number of days after the advertising ends and S is in thousands of dollars.Find the total sales for the fourth week after the advertising ends.

Determine:

The radius of a circle is growing at a rate of = .Find r as a function of t.

Determine:

Evaluate the definite integral by first finding out and then taking limit as n → ∞.(Use the right-hand endpoint of each sub-interval.)

Suppose f(x)= then find f'(x)

Use your graphing calculator to find the area between the x-axis and on the interval 1 ≤ x ≤ 3.Verify your result by finding