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4-6 Numerical integration (The Trapezoidal Rule)

4-6 Numerical integration (The Trapezoidal Rule). Ms. Battaglia – AP Calculus. Trapezoidal rule.

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4-6 Numerical integration (The Trapezoidal Rule)

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  1. 4-6 Numerical integration (The Trapezoidal Rule) Ms. Battaglia – AP Calculus

  2. Trapezoidal rule • If you need to evaluate a definite integral involving a function whose antiderivative cannot be found, then while the Fundamental Theorem of Calculus is still true, it cannot be easily applied. In this case, it is easier to resort to an approximation technique. • One way to approximate a definite integral is to use n trapezoids.

  3. The trapezoidal rule • Let f be continuous on [a,b]. The Trapezoidal • Rule for approximating is given by • Moreover, as n∞, the right-hand side • approaches

  4. Approximation with the trapezoidal rule • Use the Trapezoidal Rule to approximate with n=4

  5. Approximation with the trapezoidal rule • Use the Trapezoidal Rule to approximate with n=6

  6. Approximation with the trapezoidal rule • Use the Trapezoidal Rule to approximate • Compare the results for n=4 and n=8.

  7. Homework • Read 4.6 • Page 316 #1, 7, 11, 49a • Page 258 #86 • Page 295 #93, 94, 106 • Page 311 #129-134. • Begin studying for CH 4 test.

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