APPLICATIONS OF DEFINITE INTEGRALS
Integral as Net Change
Acceleration, Velocity, and Position
Tabular computation of distance
applet
Approximating distance traveled from velocity
using graphs
Equations of motion
applet
Accumulation functions
applet
Functions defined using integration
applet
Average Value of a Function
Average Value of a Function
problems, solutions, and explanations
Average Value
applet
Areas in the Plane
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
Area by slices
applet
Finding
area under a curve
-- visualization
Problems
finding area between curves
Areas between two curves
applet
Area Between Curves
problems, solutions, and explanations
Area Between Curves
Area Between Curves
calculator
Volumes
Solids of Revolution
plotter
Visualizing
disk, shell, washer, and cross sections methods
Volumes by disk method
Tool for
visualizing
volumes using disk method
Volume by disks
problems, solutions, and explanations
Volumes of revolution
applet
Volume
of a Solid of Revolution
Volumes, using washers
Volumes
using disks or washers
Volumes, using known cross-sections
Tool to
visualize
a cross-section (triangles)
Cross section solids
plotter
Volumes of known cross sections applet
Disks & Cross Sections
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
Shell Method
problems, solutions, and explanations
Shell Method
More Volume problems
using other methods problems, solutions, and explanations
Lengths of Curves
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
Area
of a Surface of Revolution
Several
Volume
ideas
Arc Length of a Curve
applet
A
rc Length
applet
Applications from Science and Statistics
Work
Work
Problems
More work problems
, solutions, and explanations
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
Other Applications
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
Summaries and Review Problems
Review area between curves (do
quiz 442
)
Review volumes (do
quiz 465 and 466
)
Review area, volume, and arc length ( do
quiz 471
)
Proofs of area and volume formulas