Problem Name

Problem Description

Notes

int_apps_1

If , , and , find .

int_apps_2

A quantity of gas is initially at a pressure of 500 pounds per square inch (psi) and has a volume of 1 cubic foot. The gas expands to a volume of 5 cubic feet. Find the work done by the expanding gas. Assume the perfect gas law applies; that is, assume that the pressure of the gas times its volume is constant ( ).

int_apps_3

Find the area of the region bounded by the graphs of the functions and

int_apps_4

Find the value of such that the area bounded by , the -axis, , and is .

int_apps_5

A cylindrical gasoline tank 3 feet in diameter and 4 feet long is carried on the back of a truck and is used to fuel tractors. The axis of the tank is horizontal. The opening on the tractor tank is 5 feet above the top of the tank in the truck. Find the work done in pumping the entire contents of the fuel tank into the tractor. Assume the gasoline weighs 42 pound per cubic foot.

int_apps_6

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the -axis.
 

int_apps_7

Sketch the regions bounded by the graphs of the equations and find the area of the region:

int_apps_8

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the -axis.
 

int_apps_9

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the -axis.
 

int_apps_10