Exam 6: Applications of Integration

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

Select the correct Answer for each question. -A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm.How much work is done in stretching the spring from cm to cm?

A heavy rope, ft long, weighs and hangs over the edge of a building 110 ft high.How much work is done in pulling the rope to the top of the building?

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.

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

The region bounded by the given curves is rotated about the specified axis.Find the volume of the resulting solid by any method.

Sketch the region enclosed by the curves Find the area of the region correct to two decimal places.

Find the number(s) such that the average value of the function on the interval is equal to

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.

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

Use a graphing utility to (a) plot the graphs of the given functions, (b) find the approximate x-coordinates of the points of intersection of the graphs, and (c) find an approximation of the volume of the solid obtained by revolving the region bounded by the graphs of the functions about the RoundAnswers to two decimal places.

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

Select the correct Answer for each question. -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 for each question. -Sketch the region bounded by the graphs of the given equations and find the area of that region.

The tank shown is full of water.Given that water weighs find the work (in lb-ft) required to pump the water out of the tank.

Select the correct Answer for each question. -Find the area of the shaded region.

Find the volume of the solid that is obtained by revolving the region about the line

Find the volume of the solid obtained by rotating the region bounded by about the line

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