Exam 6: Applications of Integration

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.Select the correct Answer

Select the correct Answer for each question. -Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters).You discover that both napkin rings have the same height t as shown in the figure.Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius through the center of a sphere of radius and express theAnswer in terms of

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.Select the correct Answer

The velocity v of blood that flows in a blood vessel with radius nd length at a distance from the central axis is where is the pressure difference between the ends of the vessel and is the viscosity of the blood.Find the average velocity over the interval

The velocity v of blood that flows in a blood vessel with radius and length at a distance from the central axis is where is the pressure difference between the ends of the vessel and is the viscosity of the blood.Find the average velocity over the interval

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and inequalities about the y-axis.Select the correct Answer

Select the correct Answer for each question. -Sketch the region enclosed by Find the area of the region.

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis.Sketch the region and a representative rectangle.

A spring has a natural length of cm.If a force of N is required to keep it stretched to a length of cm, how much work is required to stretch it from cm to cm?

Find the volume of a pyramid with height and base an equilateral triangle with side

Use cylindrical shells to find the volume of the solid.A sphere of radius

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Find the volume of the solid obtained by rotating about the x-axis the region under the curve from

Select the correct Answer for each question. -Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Find the area of the shaded region.

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis.Sketch the region and a representative rectangle.

Find the volume common to two spheres, each with radius if the center of each sphere lies on the surface of the other sphere.

Select the correct Answer for each question. -Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and inequalities about the

An aquarium m long, 1 m wide, and 1 m deep is full of water.Find the work needed to pump half of the water out of the aquarium.(Use the facts that the density of water is Select the correct Answer

Racing cars driven by Chris and Kelly are side by side at the start of a race.The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race.Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten seconds.