2224-Sec13_4-HWT

# 2224-Sec13_4-HWT - Math 2224 Multivariable Calculus – Sec...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 2224 Multivariable Calculus – Sec. 13.4: Double Integrals in Polar Form I. Introduction A. Formula Review x = r cos ! y = r sin ! x 2 + y 2 = r 2 B. Integrals in Polar Coordinates In polar coordinates, the natural shape to divide R into is a “polar rectangle” whose sides have constant r- and θ-values. ! A k = area of large sector - area of small sector ! A k = 1 2 r k + ! r 2 " # \$ % & ’ 2 ! ( ) 1 2 r k ) ! r 2 " # \$ % & ’ 2 ! ( = ! ( 2 r k + ! r 2 " # \$ % & ’ 2 ) r k ) ! r 2 " # \$ % & ’ 2 * + , ,- . / / ! A k = ! ( 2 r k 2 + r k ! r + ! r 2 ( ) ) r k 2 ) r k ! r + ! r 2 ( ) * +- . = ! ( 2 r k 2 + r k ! r + ! r 2 ) r k 2 + r k ! r ) ! r 2 * +- . ! A k = ! ( 2 2 r k ! r [ ] = r k ! r ! ( ! " A = r k " r " # =area of the k th piece, where r k is the midpoint ! dA = rdrd " f ( r , ¡ ) dA R ¢¢ = f ( r , ¡ ) rdrd ¡ R ¢¢ C. Area in Polar Coordinates The area of a closed and bounded region R in the polar coordinate plane is rdrd ¡ R ¢¢ ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

2224-Sec13_4-HWT - Math 2224 Multivariable Calculus – Sec...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online