1120_4 - Week 4 Outline Numerical integration The Midpoint...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Week 4 Outline Numerical integration The Midpoint Rule The Trapezoidal Rule Error estimates The Midpoint Rule The Trapezoidal Rule General formula of computing the volumes of solids Calculating the volumes of solids of revolution disk/washer method shell method Why Numerical Integration 1. It is impossible to evaluate the following integrals exactly Z 1 e x 2 d x, Z 1- 1 1 + x 3 d x. 2. The function is determined from a scientific experiment through instrument readings or collected data. There may be no formula for the function. Approximating Integrals 1. Left Endpoint Rule: Z b a f ( x )d x L n := b- a n n X k =1 f a + b- a n ( k- 1) . 2. Right endpoint Rule: Z b a f ( x )d x R n := b- a n n X k =1 f a + b- a n k . 3. Midpoint Rule: Z b a f ( x )d x M n := b- a n n X k =1 f a + b- a n ( k- 1 2 ) . 1 4. Trapezoidal Rule: Z b a f ( x )d x T n := 1 2 ( L n + R n ) = b- a 2 n ( f ( x ) + 2 f ( x 1 ) + + 2 f ( x n- 1 ) + f ( x n )) , where x k = a + b- a n k , k = 0 , 1 ...,n ....
View Full Document

This note was uploaded on 12/09/2010 for the course MATH 1120 taught by Professor Gross during the Fall '06 term at Cornell University (Engineering School).

Page1 / 4

1120_4 - Week 4 Outline Numerical integration The Midpoint...

This preview shows document pages 1 - 3. Sign up to view the full document.

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