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MAC 2233/001006 Business Calculus, Spring 2011
CRN: 12577–12582
Assistants
: V. Kumari, Y. Xi, D. Ozcan, M. Assad, T. Zerihun, A. Rai
On the Midpoint Rule for numerically estimating the value of a deFnite integral
Assume that
f
is continuous and nonnegative on the interval [
a, b
]. The defnite integral is
equal to the area oF the region “under” the graph oF
y
=
f
(
x
) From
x
=
a
to
x
=
b
. We saw
in a previous example that iF an antiderivative oF
f
can be Found, then the exact value oF the
area (and oF the defnite integral) can be obtained.
However, not all Functions
f
have easy antiderivatives. In such cases, we would use numerical
integration. There are many sophisticated methods For numerical integration. We shall consider
a very elementary method, called the Midpoint Rule, to estimate the value oF the area oF the
region bounded by
y
=
f
(
x
),
x
=
a
,
x
=
b
and
y
= 0.
So we would want to estimate the area oF shaded region in the diagram below.
b
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida  Tampa.
 Fall '08
 DANIELYAN
 Calculus

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