- Use sigma notation to represent summation.
- Use the sum of rectangular areas to approximate the area under a curve.
- Understand the notation of Riemann Sums.
- Chapter 5.1 Approximating Areas
- p. 523: 2, 12, 14-17 all
- Integration-Riemann Sums
Exit problems of the session
Compute and to approximate the area under the curve on . Explain whether it is an overestimation or underestimation.
- Sigma notation of the form is useful to express long sums of values in compact form.
- Riemann Sums are expressions of the form , and can be used to estimate the area under the curve .
- Approximate the area under the curve on the interval :
- Divide the interval into subintervals with equal length ;
- Let ;
- We can either use Left Endpoint Approximation:
or Right Endpoint Approximation:
Videos and Practice Problems of Selected Topics
- Summation notation and sums (4:26) Write and using summation notation. Expand the sum .
- * Summation notation A review with multiple-choice questions.
- Worked examples: summation notation (5:20)
- Consider the sum . Find the expression that is equal to this sum.
- Expand .
- * Practice: Summation notation. (4 problems)
- Riemann approximation introduction (6:44) Approximate the area under the curve using rectangles.
- Left and right Riemann sums (4:00) Given the graph of a function , find the left and right Riemann sums that approximate the area under between and .
- * Practice: Over and under estimation of Riemann sums. (4 problems)