4-6 Numerical integration (The Trapezoidal Rule)

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Presentation transcript:

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

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.

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

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

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

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

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.