Chapter 6 Applications of Derivatives Section 6.5 Trapezoidal Rule.

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Presentation transcript:

Chapter 6 Applications of Derivatives Section 6.5 Trapezoidal Rule

Quick Review

Quick Review Solutions

What you’ll learn about Trapezoidal approximations Comparison to other numerical approximations Bounding the error in the Trapezoidal Rule … and why Some definite integrals are best found by numerical approximations, and rectangles are not always the most efficient figures to use.

Trapezoidal Approximations

The Trapezoidal Rule

Simpson’s Rule

Error Bounds

Quick Quiz Sections 6.4 and 6.5 x 1 4 6 7 f(x) 10 30 40 20

Quick Quiz Sections 6.4 and 6.5 x 1 4 6 7 f(x) 10 30 40 20

Quick Quiz Sections 6.4 and 6.5

Quick Quiz Sections 6.4 and 6.5

Quick Quiz Sections 6.4 and 6.5

Quick Quiz Sections 6.4 and 6.5

Chapter Test

Chapter Test

Chapter Test 8. A diesel generator runs continuously, consuming oil at a gradually increasing rate until it must be temporarily shut down to have the filters replaced. Give an upper estimate and a lower estimate for the amount of oil consumed by the generator during that week. Use the Trapezoidal Rule to estimate the amount of oil consumed by the generator during that week.

Chapter Test

Chapter Test Solutions

Chapter Test Solutions

Chapter Test Solutions 8. A diesel generator runs continuously, consuming oil at a gradually increasing rate until it must be temporarily shut down to have the filters replaced. Give an upper estimate and a lower estimate for the amount of oil consumed by the generator during that week. Upper = 4.392 L; Lower = 4.008 L Use the Trapezoidal Rule to estimate the amount of oil consumed by the generator during that week. 4.2L

Chapter Test Solutions