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 # Begin studying for CH 4 test.