#### 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.

#### Solids of revolution

We use the procedure of “Slice, Approximate, Integrate” to compute volumes of
solids with radial symmetry.

#### 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.

#### Sequences as functions

A sequence can be generated by a function from the integers to the real numbers.
There are two ways to establish whether a sequence has a limit.

#### Slope fields and Euler’s method

We describe numerical and graphical methods for understanding differential
equations.