Evaluate approximately the following integral

and prove that your approximation is accurate to 8 decimal places
using the following strategy. To begin, use Maple to find a Taylor
series approximation to the function to some degree -- for example, start with a degree 5
approximation.
Evaluate the error term for this approximation by recalling from
calculus that the Taylor series error for the degree
Taylor polynomial of a function *g* on the interval [*a* - *r*, *a* + *r*]
is given by

where *M* is the maximum value
of where *t* ranges over the interval [*a* - *r*, *a* +
*r*]. Use
Maple's graphical abilities to help you obtain an upper bound for the
error term. How small does the error term have to be in order for the
integral of the Taylor approximation to to agree with

to 8 decimal places?
Explain carefully. You
may have to choose a Taylor approximation of larger degree in order
for the error term to be suffciently small for the integral to be
accurate to 8 decimal places.

In doing this problem you should be familiar with the Maple commands
`taylor` and `convert( , polynom)`. As well, you should
recall that in order to evaluate the order
derivative of a function *g* it is possible to use the command `
D@@n(g)`. In some cases, such as calculating a large iterated
derivative, you may find it convenient to suppress the output of the
calculation because it scrolls on for several screens. Remember
that this can be done by ending the command with a colon instead of a
semicolon.

Thu Mar 27 17:10:57 EST 1997