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

2. 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 – x2 = 0
Solve for x the answer:
x = -3 , x = +3 a b
Area =

3. 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) =

4. 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 =

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