Exam 6: Applications of Integration

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 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.

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.

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

A tank has the shape of an inverted right circular cone with a base radius of 4 m and a height of 9 m.If the tank is filled to a height of 1 m, find the work required (to the nearest joule) to empty the tank by pumping the water over the top of the tank.(The mass of water is 1 nd the force of gravity is )

Select the correct Answer for each question. -A tank is full of water.Find the work required to pump the water out of the outlet.

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

A bucket weighs lb and a rope of negligible weight are used to draw water from a well that is ft deep.The bucket starts with 50 lb of water and is pulled up at a rate of 10 ft/s, but water leaks out of a hole in the bucket at a rate of 0.5 lb/s.Find the work done in pulling the bucket to the top of the well.Select the correct Answer

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

Find the work done in pushing a car a distance of while exerting a constant force of

If J of work are needed to stretch a spring from cm to cm and another J are needed to stretch it from cm to cm, what is the natural length of the spring? Round theAnswer to nearest integer.

Find the area of the shaded region.

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

A chain weighing 4 lb/ft hangs vertically from a winch located 11 ft above the ground, and the free end of the chain is just touching the ground.Find the work done by the winch in pulling in the whole chain.

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

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.

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

Sketch the region enclosed by Find the area of the region.Select the correct Answer

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