Evaluating a Definite Integral as a Limit In Exercises 5-10, evaluate the definite integral by the limit definition.
To calculate: Definite integral of by the limit definition.
Formula used: Formula for the definite integral of from to :
Here is the lower limit of integration and is the upper limit of integration.
The sum of a constant times is written as:
Here is a constant.
Calculation: The function can be integrated on the interval because it is continuous on .
Definition of integrability implies that any partition whose norm approaches can be used to determine the limit.
For computational convenience, define by subdividing into subintervals of equal width as:
Choose as the right endpoints of each subinterval. Therefore,
So, the definite integral is:
Use value of and
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