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by: Josh Benton

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6

# Calculus II Section 6.1 Notes - Area Between Curves MAC2312

Marketplace > Santa Fe Community College > Math > MAC2312 > Calculus II Section 6 1 Notes Area Between Curves
Josh Benton
FSU

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These notes show how to find the area between curves using integration.
COURSE
Calculus 2
PROF.
Hallie Dilley
TYPE
Class Notes
PAGES
6
WORDS
CONCEPTS
Calculus, Calc, calculus 2, Calc 2, area, curves, area between curves
KARMA
Free

## Popular in Math

This 6 page Class Notes was uploaded by Josh Benton on Tuesday March 22, 2016. The Class Notes belongs to MAC2312 at Santa Fe Community College taught by Hallie Dilley in Spring 2016. Since its upload, it has received 18 views. For similar materials see Calculus 2 in Math at Santa Fe Community College.

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Date Created: 03/22/16
Section 6.1 - Areas Between Curves Class Notes Even and Odd Functions 1. Even Function: Even functions are symmetrical about the . 2. Odd Function: Odd functions are symmetrical about the . De▯nite Integrals 1. If f(x) is an even function, then Z Z Z a a 0 f(x) dx = 2 f(x) dx = 2 f(x) dx ▯a 0 ▯a 2. If f(x) is an odd function, then Z a f(x) dx = 0 ▯a Section 6.1 - Areas Between Curves Class Notes Visual: Theorem: If f(x) and g(x) are both continuous on [a;b] and f(x) ▯ g(x), then Z b A = [f(x) ▯ g(x)] dx a where A is the area between the curves. Z Z Z b b b Note: [f(x) ▯ g(x)] dx = f(x) dx ▯ g(x) dx a a a Section 6.1 - Areas Between Curves Class Notes Example: Find the area between the region bounded by y = x and 1 y = 2 ▯ x . 2 2 Section 6.1 - Areas Between Curves Class Notes Additional Cases: 1. Note: Set up the integrand so that you have the top function minus the bottom function. Section 6.1 - Areas Between Curves Class Notes 2. A = A = Note: Set up the integrand so that you have the right function minus the left funciton. Section 6.1 - Areas Between Curves Class Notes Example: Find the area enclosed by the given curves: 2 2 x 1 7y ; x = 1 2 6y

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