1. Section 4.2A Calculus AP/Dual, Revised ©2018 viet.dang@humbleisd.net
Trapezoidal Area
Section 4.2A
Calculus AP/Dual, Revised ©2018
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§4.2A: Trapezoidal Sum

2. Review Find the area of the trapezoid. 2/25/2019 7:22 AM
§4.2A: Trapezoidal Sum

3. Trapezoidal Area (Uneven Area)
Find the area of the curve using the trapezoid sum.
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§4.2A: Trapezoidal Sum

4. Trapezoidal Rule
To evaluate a definite integral involving a function whose anti-derivative cannot be found
Integral: 𝒂 𝒃 𝒇 𝒙 𝒅𝒙 = 𝟏 𝟐 𝒃−𝒂 𝒏 𝑳 𝒏 + 𝑹 𝒏
Area of Trapezoidal Rule:
𝟏 𝟐 𝒙 𝒇 𝒙 𝟎 +𝒙𝟏 +𝒇 𝒙 𝟏 +𝒙𝟐 +…+𝒇 𝒙 𝒏−𝟏 +𝒙𝒏
𝒙= 𝒃−𝒂 𝒏
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§4.2A: Trapezoidal Sum

5. Example 1
Use the Trapezoidal Rule to approximate the value of 𝟏 𝟓 𝒙 𝟐 +𝟑 𝒅𝒙 for 𝒏=𝟒.
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§4.2A: Trapezoidal Sum

6. Example 1
Use the Trapezoidal Rule to approximate the value of 𝟏 𝟓 𝒙 𝟐 +𝟑 𝒅𝒙 for 𝒏=𝟒.
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§4.2A: Trapezoidal Sum

7. Example 1
Use the Trapezoidal Rule to approximate the value of 𝟏 𝟓 𝒙 𝟐 +𝟑 𝒅𝒙 for 𝒏=𝟒. Solve using FTC:
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§4.2A: Trapezoidal Sum

8. Example 2
Use the Trapezoidal Rule to approximate the value of 𝟏 𝟑 𝟒−𝒙 𝟐 𝒅𝒙 for 𝒏=𝟒.
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§4.2A: Trapezoidal Sum

9. Your Turn
Use the Trapezoidal Rule to approximate the value of 𝟏 𝟗 𝒙 𝟐 𝒅𝒙 for 𝒏=𝟒.
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§4.2A: Trapezoidal Sum

10. Review Use the Left Hand Sum to approximate the value of 𝟏 𝟕 𝒇 𝒙 𝒅𝒙 .𝟐 𝟓 𝟔 𝟕
𝒇 𝒙 𝟑 −𝟏 𝟒 𝟖
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§4.2A: Trapezoidal Sum

11. Example 3
Use the Trapezoidal Rule to approximate the value of 𝟏 𝟕 𝒇 𝒙 𝒅𝒙 𝒙 𝟏 𝟐 𝟓 𝟔 𝟕
𝒇 𝒙 𝟑 −𝟏 𝟒 𝟖
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§4.2A: Trapezoidal Sum

12. Your Turn
Use the Trapezoidal Rule to approximate the value of 𝟏 𝟏𝟑 𝒇 𝒙 𝒅𝒙 . 𝒙 𝟏 𝟑 𝟖 𝟏𝟐 𝟏𝟑
𝒇 𝒙 𝟐 𝟓 𝟒
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§4.2A: Trapezoidal Sum

13. AP Multiple Choice Practice Question 1 (non-calculator)
The graph of 𝒇 is shown below. Approximate 𝟐 𝟏𝟐 𝒇 𝒙 𝒅𝒙 using the trapezoid approximation. (A) 𝟒𝟒 (B) 𝟖𝟖 (C) 𝟏𝟏𝟐 (D) 𝟐𝟐𝟒
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§4.2A: Trapezoidal Sum

14. AP Multiple Choice Practice Question 1 (non-calculator)
The graph of 𝒇 is shown below. Approximate 𝟐 𝟏𝟐 𝒇 𝒙 𝒅𝒙 using the trapezoid approximation.
Vocabulary
Process and Connections
Answer
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§4.2A: Trapezoidal Sum

15. Assignment
Worksheet
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§4.2A: Trapezoidal Sum