Exam 6: Applications of Integration

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Select the correct Answer for each question. -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.

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. the line y = 3

Find the volume of the solid obtained by revolving the region under the graph of on about the

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.

Find the number b such that the line divides the region bounded by the curves and into two regions with equal area.

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

Select the correct Answer for each question. -A particle moves a distance of 160 ft along a straight line.As it moves, it is acted upon by a constant force of magnitude 10 lb in a direction opposite to that of the motion.What is the work done by the force?

Find the average value of the function on the given interval.

The base of a solid is a circular disk with radius Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.Select the correct Answer

The base of a solid is a circular disk with radius Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

Select the correct Answer for each question. -Find the volume of the solid obtained by rotating the region bounded by about the x-axis.

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

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.

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?

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region about the indicated axis or line.

A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 c m.How much work is done in stretching the spring from cm to cm?

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