APPLICATIONS OF DEFINITE INTEGRALS

• Acceleration, Velocity, and Position

• Review problems for finding the area between two curves--Go to Calculus Book II,  then Applications of Integration, then Area, then Area Between Two Curves I or Area Between Two Curves II
• Visualizing an area problem
• Finding area under a curve -- visualization
• Problems finding area between curves
• Areas between two curves applet

• Instructions for using your calculator to generate 3-D graphs
• Volumes by disk method
• Tool for visualizing volumes using disk method
• The volume of revolution generated by the region between the x-axis and the curve
y = Sqrt[x], with x between 1 and 4.
• The volume of revolution that results when the region between the x-axis and the curve
  y = 2/(1 + (x - 2)^2) is revolved about the x-axis
• Approximating volumes of solids of revolution experiment
• Volumes, using washers
• Volumes using disks or washers
• Volumes, using known cross-sections
• Tool to visualize a cross-section (triangles)
• Tool to visualize a cross-section with circular base (squares)
• Computing the volume of water in a tipped glass (scroll down to the third area)
• Calculating the volume of the intersection of two cylinders (scroll to the end)
• Volumes, using shells
• Problems using the shell method

• Review problems for finding arclength -- Go to Calculus Book II, then Applications of Integration, then Assorted Applications, then Arc Length
• Another Tool for computing the arclength of a curve
• Tutorial for arc length
• Surface Area of Revolution discussion
• Several Volume ideas
• Arc Length of  a Curve applet

• Work
• Work Problems
• The Great Molasses Flood of 1919
• Work discussion
• Probability Densities
• Probability Densities
• Means, Medians, & Averages
• Normal Distribution
• Moments and Centroids
• Centers of Mass
• Problems finding the center of gravity
• More problems on moments and centroids
• Centroid demo

• Minimum Value of the Integral of a Function
• Minimum Value of an Integral applet
• Average Value of a Function
• Finding average value of a function
• Average Value of a Function

• Review area between curves (do quiz 442)
• Review volumes (do quiz 465 and 466)
• Review area, volume, and arc length ( do quiz 471)
  

Go to Calculus Lessons Page
Go to Calculus Page