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3.2

# Calculus: Trapezoid and Midpoint Rules

by Texas Instruments

#### Objectives

• Identify whether rectangle or trapezoidal approximations will provide an overestimate or an underestimate of the area under a curve from a positive function graph
• Order the estimates of area under a curve
• Describe the relationship of concavity to the midpoint and trapezoidal approximations

#### Vocabulary

• trapezoidal approximations
• left, right, and midpoint rectangle approximations
• area under a curve

#### About the Lesson

This lesson involves providing students with a visual representation of area estimation methods in order to determine which is most accurate. As a result, students will:

• Observe the left endpoint rectangle, right endpoint rectangle, and trapezoidal estimates of the area under the curve in order to observe and make predictions about the accuracy of each estimate.
• Experience a dynamic comparison of the midpoint rectangle and trapezoidal estimates of area under a curve, relating these to the concavity of the curve.
• Suggest their own geometric estimation methods for area under a curve to improve on the accuracy of the midpoint rectangle estimate.