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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.