Presentation is loading. Please wait.

Presentation is loading. Please wait.

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.

Similar presentations


Presentation on theme: "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."— Presentation transcript:

1 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.

2 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 |

3 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 =

4 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 [] = =

5 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

6 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 =


Download ppt "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."

Similar presentations


Ads by Google