Further Techniques and Applications of the Integral

Note! If your screen is not partitioned into three frames, press here to bring up the frames that will enable you to use these quizzes.

The integral of a product is the product of the integrals.

When using integration by parts, it is often best to pick something easy to integrate to go in the "I" column.

When using integration by parts, you have to get it right the first time.

To use a table of integrals, your integral must appear in the table.

When using a table of integrals, you may have to make a substitution to turn your integral into one that appears in the table.

When using a table of integrals, you may have to do some algebra to turn your integral into one that appears in the table.

To find the area between the graphs of f and g, integrate the absolute value of their difference.

To find the area between the graphs of f and g, integrate the larger minus the smaller where possible.

If the graphs of f and g cross midway between a and b, then

b

a

(f(x)

g(x))

10.

The consumers' surplus represents the total amount that consumers save by paying a lower price.

11.

The producers' surplus represents the amount extra that each producer will earn by charging a higher amount.

12.

The average of f on [a, b] is (f(a)+f(b))/2.

13.

The moving average of f tends to be more volatile than f itself.

14.

A moving average of f shows long-term trends in f more clearly.

15.

f(x) dx

F(a) if F' = f.

16.

f(x) dx

does not always exist.

17.

b

a

f(x) dx

always exists.

18.

x f'(x) = x² + 1 is a differential equation.

19.

x f(x) = x² + 1 is a differential equation.

20.

x f'(x) = x² + 1 has as a solution f(x) = x + ln x + C.

True/False Quizzes for Applied Calculus Topic: Further Techniques and Applications of the Integral (Chapter 7)