#### A review of integration techniques

We review common techniques to compute indefinite and definite integrals.

#### Area between curves

We introduce the procedure of “Slice, Approximate, Integrate” and use it study the
area of a region between two curves using the definite integral.

#### Accumulated cross-sections

We can also use the procedure of “Slice, Approximate, Integrate” to set up integrals
to compute volumes.

#### What is a solid of revolution?

We define a solid of revolution and discuss how to find the volume of one in two
different ways.

#### The washer method

We use the procedure of “Slice, Approximate, Integrate” to develop the washer
method to compute volumes of solids of revolution.

#### The shell method

We use the procedure of “Slice, Approximate, Integrate” to develop the shell method
to compute volumes of solids of revolution.

#### Length of curves

We can use the procedure of “Slice, Approximate, Integrate” to find the length of
curves.

#### Physical applications

We apply the procedure of “Slice, Approximate, Integrate” to model physical
situations.

#### Integration by parts

We learn a new technique, called integration by parts, to help find antiderivatives of
certain types of products by reexamining the product rule for differentiation.

#### Trigonometric integrals

We can use substitution and trigonometric identities to find antiderivatives of certain
types of trigonometric functions.

#### Improper Integrals

We can use limits to integrate functions on unbounded domains or functions with
unbounded range.

#### Representing sequences visually

We can graph the terms of a sequence and find functions of a real variable that
coincide with sequences on their common domains.

#### The Dot Product

The dot product is an important operation between vectors that captures geometric
information.

#### Projections and orthogonal decomposition

Projections tell us how much of one vector lies in the direction of another and are
important in physical applications.

#### The cross product

The cross product is a special way to multiply two vectors in three-dimensional
space.

#### Parameterizing by arc length

We find a new description of curves that trivializes arc length computations.

#### Functions of several variables

We introduce functions that take vectors or points as inputs and output a
number.

#### Open and Closed Sets

We generalize the notion of open and closed intervals to open and closed sets in
.