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Definite Integrals Evaluated

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Consider the definite integral I

I = ∫ e^x dx

1. evaluate the integral I directly by use of a suitable anti-derivative.

2. evaluate the integral I by use of a suitable Riemann sum and formally limiting that sum

3. evaluate the integral I by use of the trapezoidal rule:
a) I T,2 - for 2 sub-intervals
b) I T,4 - for 4 sub-intervals
c) I T,8 - for 8 sub-intervals

4. evaluate the intergral I by use of simpson's rule:
a) I S,2 - for 2 sub-intervals
b) I S,4 - for 4 sub-intervals
c) I S,8 - for 8 sub-intervals

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The expert evaluates the integral by use of simpson's rules are determined.

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