Unit 8: Applications of Integration

Find the arc length of [math] from [math] to [math].

The area of the region bounded by [math] and [math] is

The volume of the solid formed by revolving the region bounded by [math], [math], and [math] about the [math]-axis is

The volume of the solid with known cross sections that are squares perpendicular to the [math]-axis, where the base is bounded by [math] and [math] from [math] to [math], is

The average value of [math] on [math] is

The volume of the solid generated by revolving the region bounded by [math] and [math] about the [math]-axis is

The length of the curve [math] from [math] to [math] is given by

The area between [math] and the [math]-axis from [math] to [math] is:

Find the area between [math] and [math] from [math] to [math].

Find the volume when [math] is revolved about the [math]-axis from [math] to [math] using the disk method.

The average value of [math] on [math] is:

A solid has base bounded by [math] and [math] from [math] to [math]. Cross sections perpendicular to the [math]-axis are squares. Find the volume.

Using the washer method, find the volume when the region between [math] and [math] is revolved about the [math]-axis.

Find the arc length of [math] from [math] to [math].

Using the shell method, find the volume when [math] from [math] to [math] is revolved about the [math]-axis.

The base of a solid is the region bounded by [math] and [math]. Cross-sections perpendicular to the x-axis are squares. What integral gives the volume?

The length of the curve [math] from [math] to [math] is given by

The region R is bounded by [math], [math], and [math]. What is the volume of the solid generated when R is revolved about the x-axis?