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2224-Sec13_3-HWT

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

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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. B. Area of a Region Between Two Curves - Integrating with respect to y .

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