Exam 6: Applications of Integration

Solve the problem. -A spring on a horizontal surface can be stretched and held 0.5 m from its equilibrium position with a force of 45 N. How much work is done in stretching the spring 3 m from its equilibrium position?

Solve the problem. -After a new firm starts in business, it finds that its rate of profits (in hundreds of dollars per year) after t years of operation is given by Find the profit in year 8 of the operation.

Find the length of the curve. -y = from x = 1 to x = 8

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. -The region bounded by y = 6 , y = 6, and x = 0 about the line y = 6

Find the area of the surface generated when the given curve is revolved about the x-axis. -y = on

Set up an integral for the length of the curve. -y = , - $\le$ x $\le$

Find the area enclosed by the given curves. -y = sin x, y = x, $\le$ x $\le$

Find the length of the curve. -y = + from x = 1 to x = 5

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the x-axis

Solve the problem. -Find the volume that remains after a hole of radius 1 is bored through the center of a solid cylinder of radius 5 and height 10.

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. -x = 3 , x = - 3y, y = 1