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Published byKelli Jessel Modified over 2 years ago

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1 3.6 Area enclosed by the x-axis Areas above the x-axis give a positive Definite Integral Areas below the x-axis give a negative Definite Integral We always think of area as positive. Therefore Area = | a b f(x).dx | Always sketch the area to be found.

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2 3.6 Area enclosed by the x-axis Some functions have area above and below the x-axis. a b c The Definite Integral | a c f(x).dx | < Area. Therefore Area = | a b f(x).dx | + | b c f(x).dx |

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3 3.6 Area enclosed by the x-axis Example 1: Find the area between y = x 2 – 4 and x-axis. x 2 – 4 = 0 x 2 = 4 x = ± (x 2 -4).dx -2 2 x33x33 [] - 4x -2 2 = [] - 4x2 = [] - 4x(-2) - ≈ |-10.7| ≈ 10.7 Area =

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4 3.6 Area enclosed by the x-axis Example 2: Find the area between y = x 3 and x-axis from -1 to 1. x 3.dx 0 x44x44 [] 0 = Area = x 3.dx x44x44 [] = =

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5 3.6 Area enclosed by the x-axis For Odd Functions -a a f(x).dx = 0 -a a f(x).dx < 0 For Even Functions -a a 0 a 0 So for Odd & Even Functions -a a f(x).dx = 0 a 2 f(x).dx

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6 3.6 Area enclosed by the x-axis Example 2: Find the area between y = x 3 and x-axis from -1 to 1. x44x44 0 = 2x [] 1 Area = = x 3.dx 0 1 2x 1414 =

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