Langara College - Department of Mathematics and Statistics

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Internet Resources for the Calculus Student - Topics in Calculus

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Applications of Integration

In addition to their use for calculating areas,
definite integrals also arise in all sorts of problems involving accumulation
or total amounts of various quantities.
At the Manipula
Math with Java site in Japan there are several applets demonstrating
how the volume
of a Solid of Revolution corresponds to a limit of Riemann sums. The
JAVA applet allows a curve to be rotated about the *x*-axis. Cross-sections
can be highlighted and shifted, and the number of disks making up the volume
increased or decreased, and then the cross-sectional area and the volume
are calculated.

Our 'raw list' (of links provided without comment) includes many more
examples of sites demonstrating applications of integration, including
more volumes, arc length, some applied sciences, and probability and statistics.

In many of these examples, once we have used the Riemann sum idea to
see that what we want is really an integral, that integral is then
most easily calculated by using the Fundamental Theorem of Calculus to
reduce it to an antiderivative problem.

But sometimes we really do want to go the other way. For example, if
the velocity of an object has been measured at certain instants of time,
is it possible to "integrate" this discrete data to estimate the change
in the object's position? This idea is explored in the page on Accumulating
Rates of Change, in the Gallery
of Interactive Geometry, at the University of Minnesota's Geometry
Center.

If you have come across any good web-based illustrations of these and
related concepts,

please do let
us know and we will add them here.