#### 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.

#### Surface areas of revolution

We compute surface area of a frustrum then use the method of “Slice, Approximate,
Integrate” to find areas of surface areas of revolution.

#### 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 alternating series test

Alternating series are series whose terms alternate in sign between positive and
negative. There is a powerful convergence test for alternating series.

#### Putting it all together

This section reinforces and synthesizes the ideas about sequences and series.

#### Slope fields and Euler’s method

We describe numerical and graphical methods for understanding differential
equations.

#### Separable differential equations

Separable differential equations are those in which the dependent and independent
variables can be separated on opposite sides of the equation.

#### The Dot Product

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