Calculus 1, Chapter 5 Study Guide
Prepared by Dr. Robert Gardner
The following is a brief list of topics covered in Chapter 5 of Thomas’
Calculus. Test questions will be chosen directly from the text. This list is
not meant to be comprehensive, but only gives a list of several important
topics. I reserve the right to ask you definitions and theorems on the tests.
If I do so, then I will choose from the bold-faced items below.
5.1 Area and Estimating with Finite Sums. No!
5.2 Sigma Notation and Limits of Finite Sums. Sigma notation,
Riemann sums (and included components such as partition and subin-
terval), norm.
5.3 The Definite Integral. Definite integral, difference between
definite integral/indefinite integral/antiderivative, integrability of con-
tinuous functions and properties of definite integrals (Theorems 1 and
2), regular partition and use to calculate definite integrals, area under
a curve, average value of a function.
5.4 The Fundamental Theorem of Calculus. Mean Value The-
orem for Definite Integrals, Fundamental Theorem of Calcu-
lus, Parts 1 and 2, the Net Change Theorem.
5.5 Indefinite Integrals and the Substitution Method. u-substi-
tution (“The Substitution Rule”).
5.6 Substitution and Area Between Curves. Area between curves,
dx and dy slices.