2224-Sec13_3-HWT

# 2224-Sec13_3-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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

Math 2224 Multivariable Calculus – Sec. 13.3: Area by Double Integration I. Review from 1206 A. Area Between the Curves Using Vertical Rectangles; Integrating wrt x 1. If f and g are continuous on [ a,b ] and g(x) < f(x) for all x in [ a,b ], then the area of the region bounded by the graphs of f and g and the vertical lines x=a and x=b is A = f x ( ) ! g x ( ) [ ] a b " dx ; where f(x) is the upper curve & g(x) is the lower curve. 2. Steps to Find the Area Between Two Curves (wrt x ) a. Graph the curves and draw a representative rectangle. This reveals which curve is f (upper curve) and which is g (lower curve). It also helps find the limits of integration if you do not already know them. b. Find the limits of integration; you may need to find the pts of intersection. c. Write a formula for f(x)–g(x). Simplify it if you can. d. Integrate [ f(x)–g(x) ] from a to b . The number you get is the area.

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.

## This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

### Page1 / 4

2224-Sec13_3-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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

View Full Document
Ask a homework question - tutors are online