sn3_1 - Math 1432 Notes Session 3 Homework questions: Hw7...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 1432 Notes – Session 3 Homework questions: Hw7
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Section 8.7 – Numeric Integration Sometimes there are integrals you cannot compute by any method. In those cases we need to use numeric integration. Methods from Calc I: Left endpoints: Right endpoints: Midpoints: Summary:
Background image of page 2
New methods: Trapezoids: Simpson’s rule (parabolic estimate) Example: Approximate 3 2 1 x dx using the Trapezoid Rule with n=4
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Approximate 3 2 1 x dx using Simpson’s Rule with n=4 You Try! (hw8 #1) If the trapezoid method is used to estimate ( 29 f 5 2 x dx , with n = 30, then the width (height) of each trapezoid will be 3/10. a. True b. False
Background image of page 4
Error Estimates: Since all of the methods above give estimates of the integrals, we need to know how close we are to the real answer. We will face two types of errors: theoretical error (the error that is inherent in the method we use) and round-off error. The theoretical error for the trapezoid rule is ) ( ' ' 12 ) ( 2 3 c f n a b E T n - - = where c is some number between a and b . If f’’ is bounded on [ a, b ], M x f ) ( ' ' for b x a then M n a b E T n 2 3 12 ) ( - = Estimate the error if the Trapezoid rule is used to find 3 1 sin xdx using n=10. The theoretical error for Simpson’s rule is ) ( 2880 ) ( ) 4 ( 4 5 c f n a b E S n - - = where c is some number between a and b . If f (4) is bounded on [ a, b ], M x f ) ( ) 4 ( for b x a then M n a b E S n 4 5 2880 ) ( - =
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/07/2012 for the course MATH 11278 taught by Professor Jeffmorgan during the Summer '10 term at University of Houston.

Page1 / 26

sn3_1 - Math 1432 Notes Session 3 Homework questions: Hw7...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online