5.5 Trapezoidal Rule.

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Presentation transcript:

5.5 Trapezoidal Rule

Quick Review

Quick Review Solutions

What you’ll learn about Trapezoidal Approximations Other Algorithms Error Analysis Essential Question How do we find definite integrals that are not best found by numerical approximations, and rectangles are not always the most efficient figures to use?

Trapezoidal Approximations

The Trapezoidal Rule

Example Using Trapezoidal Rule Use the Trapezoidal Rule with n = 4 to approximate the value of the integral. Use the concavity of the function to predict whether the approximation is an overestimate or an underestimate. Concave Down underestimate

Simpson’s Rule

Example Using Simpson’s Rule Use Simpson’s Rule with n = 4 to approximate the value of the integral. Find the integral’s exact answer to check your answer.

Error Bounds and

Pg. 312, 5.5 #1-19 odd