Finding the Total Area y= 2x +1 y= x3 2 5 2 5 Area = Area =

Example: Find the area under the graph y= 9 – x2 and above the x-axis Area = y What are the coordinates for a and b? y= 9 – x2 They are the x-intercepts, So They both have y = 0, From To y= 0 Then 9 – x2 = 0 Solve for x the answer: x = -3 , x = +3 a b Area =

Finding the Area Between Two Curves y= f(x) a b y= g(x) y= f(x) a b y= g(x) y= f(x) a b y= g(x) Area between f(x) and g(x) Area under f(x) = Area under g(x) =

They are the intercept points, Example: Find the area between the graph y= 9 – x2 and y = x2 + 1 Area Between = The difference of the two areas y y= x2 + 1 y= 9 – x2 a b What are the coordinates for a and b? They are the intercept points, same y and same x y = y 9 – x2 = x2 + 1 Solve for x, the answer: x = -2 , x = +2 Area =

Example: Find the area under the graph y= x2 - 9 between x = -5 and x= 3 Total Area = y Or, Total Area y= x2 – 9 A= 14.67 A= -36 Total Shaded Area = 14.67 + 36 = 50.67 -5 -3 3