In this section, we will begin to look at Σ notation and how it can be used to represent Riemann sums (rectangle approximations) of definite integrals.

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Presentation transcript:

In this section, we will begin to look at Σ notation and how it can be used to represent Riemann sums (rectangle approximations) of definite integrals.

Summation or Sigma notation is defined by:

Find each of the following sums: (a) (b) (c)

The following are sums with which we will need to work:

(a) Use sigma notation to express R 10 for and then evaluate it. (b) Use sigma notation to express L 20 for and then evaluate it.

Recall that the definite integral can be defined as a limit of sums: where the c k are determined by whether we are using left, right, or midpoint rectangles.

(a) Give the summation notation of R n for and simplify the result. (b) Use the limit definition of the definite integral to evaluate.

(a) Give the summation notation of R n for and simplify the result. (b) Use the limit definition of the definite integral to evaluate.

Evaluate the indicated limit by rewriting it as a definite integral and using the F.T.C.