James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

6
Applications of Integration
When a bat strikes a baseball,
the collision lasts only about
a thousandth of a second. In
the project on page 464, you
will use calculus to find the
average force on the bat when
this happens. Several other
applications of calculus to
the game of baseball are
explored as well.
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In THIS chapter we explore some of the applications of the definite integral by using it to
compute areas between curves, volumes of solids, and the work done by a varying force. The
common theme is the following general method, which is similar to the one we used to find areas
under curves: we break up a quantity Q into a large number of small parts. We next approximate
each small part by a quantity of the form f sx i *d Dx and thus approximate Q by a Riemann sum.
Then we take the limit and express Q as an integral. Finally we evaluate the integral using the
Fundamental Theorem of Calculus or the Midpoint Rule.
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