Exam 6: Applications of Integration

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 about the x-axis.

The height of a monument is A horizontal cross-section at a distance meters from the top is an equilateral triangle with side meters.Find the volume of the monument.

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 about the indicated line. , y = 0; the line y = 5

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? Select the correct Answer

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 p 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 D and express theAnswer in terms of Select the correct Answer

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.Sketch the region and a representative rectangle.

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the specified axis.Select the correct Answer

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.

Select the correct Answer for each question. -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. the x-axis

Sketch the region bounded by the graphs of the given equations and find the area of that region.

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 d through the center of a sphere of radius D 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

Select the correct Answer for each question. -Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

Select the correct Answer for each question. -Newton's Law of Gravitation states that two bodies with masses attract each other with a force where r is the distance between the bodies and G is the gravitation constant.If one of bodies is fixed, find the work needed to move the other from r=l to r=g .

Find the volume of the solid obtained by rotating the region bounded by about the x-axis.

Sketch a graph to estimate the x-coordinates of the points of intersection of the given curves.Then use this information to estimate the volume of the solid obtained by rotating about the y axis the region enclosed by these curves.Rounded to the nearest hundredth.

Use the Midpoint Rule with to estimate the volume obtained by rotating about the region under the y-axis the region under the curve. The choices are rounded to the nearest hundredth.Select the correct Answer

Use integration to find the area of the triangle with the given vertices.Select the correct Answer(0, 0), (1, 7), (4, 2)

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.Sketch the region and a representative rectangle.