{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

View Full Document Right Arrow Icon
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 .
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern