1 / 7

Section 5.3: Finding the Total Area

y. y. y = f ( x ). y = g ( x ). x. x. a. b. a. b. Shaded Area =. Shaded Area =. Section 5.3: Finding the Total Area. y= f ( x ). y= f ( x ). y= f ( x ). y = g ( x ). y = g ( x ). a. a. b. b. y = g ( x ). Area under f ( x ) =. Area under g ( x ) =. a. b.

ina
Download Presentation

Section 5.3: Finding the Total Area

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. y y y = f(x) y = g(x) x x a b a b Shaded Area = Shaded Area = Section 5.3: Finding the Total Area

  2. y= f(x) y= f(x) y= f(x) y = g(x) y = g(x) a a b b y = g(x) Area under f(x)= Area under g(x)= a b A) Area Between Two Curves in [a , b] Area between f(x)and g(x)

  3. y y = g(x) y y = f(x) y = 0 y = 0 a b x x a b B) Area Between a Curve and the x-Axis in [a , b] x-Axis is same as y = 0 Top Function is y = 0 Top Function is y = f(x) Bottom Function is y = g(x) Bottom Function is y = 0 Area under f(x) in[a , b]: Area under g(x) in[a , b]:

  4. y y = 2x- 1 y = x2 - 4 x b a C) Area Between Intersecting Curves Example: Find the area between the graph y= x2 - 4and y = 2x- 1 1) Graph both functions 2) Find the points of intersection by equating both functions: y = y x2 - 4 = 2x- 1 x2 - 2x- 3 = 0 (x+ 1)(x- 3) = 0 x = -1 , x = +3 3) Area Top Function is 2x- 1, Bottom Function is x2 - 4

  5. y y = x2 - 4x +3 x 1 3 y = 0 Example: Find the area between the graph y = x2 -4x + 3and the x-axis 1) Graph the function with the x-axis (or y = 0) 2) Find the points of intersection by equating both functions: y = y x2 -4x + 3= 0 (x- 1)(x- 3) = 0 x = 1 , x = 3 3) Area Top Function is y = 0, Bottom Function is y = x2 -4x + 3

  6. y= x2 – 4 y y = 0 3 -1 -2 2 x A2= 2.33 A1= 9 = 9 + 2.33 = 11.33 D)Area Between Curves With Multiple Points of Intersections (Crossing Curves) Example: Find the area enclosed by the x-axis, y = x2 - 4, x = -1 and x = 3 1) Graph the function y = x2 - 4 with the x-axis (or y = 0), Shade in the region between x = -1 and x = 3 2) Find the points of intersection by equating both functions: y = y or (x- 2)(x+ 2) = 0 x2 -4= 0 x = 2 , x = -2 y = x2 - 4 and the x-axis cross each others x = -2, x = 2 3) Area

  7. y = x3 y y = x x 1 -1 0 A2= 0.25 A1= 0.25 , the answer will be zero. Note: if you write Area = Example: Find the area enclosed by y = x3 and y = x 1) Graph the function y = x3 , and y = x 2) Find the points of intersection by equating both functions: y = y or x3 - x = 0 x3 = x x(x2 - 1) = 0 x(x- 1)(x + 1) = 0 x = 0 , x = -1 , x = 1 The graphs cross at x = -1, x = 0 and x = 1 3) Area = 0.5 + 0.25 = 0.25

More Related