Unit 8: Applications of Integration

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

Find the area of the region enclosed by [math] and [math].

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

Find the volume of the solid generated by revolving [math] about the x-axis from [math] to [math].

Which integral represents the volume of the solid formed by revolving [math] about the y-axis from [math] to [math]?

Find the volume of the solid generated by revolving the region between [math] and [math] about the x-axis from [math] to [math] (washer method). Express as a fraction of [math] (give the coefficient).

A particle moves along the x-axis with velocity [math] for [math]. What is the displacement of the particle?

Using the shell method, which integral gives the volume when [math] (for [math]) is revolved about the y-axis?

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

The volume of the solid formed by revolving [math] about the [math]-axis from [math] to [math] is

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

A particle moves along the [math]-axis with velocity [math] for [math]. The total distance traveled by the particle is

If the position of a particle is [math], at what time [math] does the particle change direction?

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

A particle moves along the x-axis with velocity [math] for [math]. What is the total distance traveled by the particle from [math] to [math]?

The region [math] is bounded by [math] and [math]. When [math] is revolved about the [math]-axis, which integral gives the volume using the washer method?