APPLICATIONS OF DEFINITE INTEGRALS
Integral as Net Change
Acceleration, Velocity, and Position
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
Finding
area under a curve
-- visualization
Problems
finding area between curves
Areas between two curves
applet
Volumes
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
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
Several
Volume
ideas
Arc Length of a Curve
applet
Applications from Science and Statistics
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
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
)
Go to
Calculus Lessons Page
Go to
Calculus Page