Learning Outcomes

1. Use sigma notation to represent summation.
2. Use the sum of rectangular areas to approximate the area under a curve.
3. Understand the notation of  Riemann Sums.

Textbook

• Chapter 5.1  Approximating Areas

Textbook Assignment

• p. 523:    2, 12, 14-17 all

WeBWork Assignment

• Integration-Riemann Sums

Exit problems of the session

1. Compute and to approximate the area under the curve on . Explain whether it is an overestimation or underestimation.

Key Concepts

• 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 :
1. Divide the interval into subintervals with equal length ;
2. Let ;
3. We can either use Left Endpoint Approximation: or Right Endpoint Approximation #### Videos and Practice Problems of Selected Topics

1. Summation notation and sums (4:26) Write and using summation notation.  Expand the sum .
2. * Summation notation A review with multiple-choice questions.
3. Worked examples: summation notation (5:20)
• Consider the sum . Find the expression that is equal to this sum.
• Expand .
4. * Practice: Summation notation. (4 problems)
5. Riemann approximation introduction (6:44) Approximate the area under the curve using rectangles.
6. 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 .
7. * Practice: Over and under estimation of Riemann sums. (4 problems)

#### STEM Application

MAT1475 Optimization Assignment