AREA BETWEEN CURVES
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The graph below shows two functions:
The graphs intersect at two distinct points, (0,0) and (9,6).
To arrive at a trapezoidal approximation for the area, the function values along each graph must be calculated:
To determine the AREA of each trapezoid, we average the bases. The value of each base is the difference of the function values. Since the graph of f(x) is above the graph of g(x), they are subtracted in that order.
The height of each trapezoid is the incremental width of the graph - in this case, 1.
The trapezoidal approximation of the area is 8.64 units.
Let's look at another set of intersecting functions:
QUESTIONS TO CONSIDER
- Use this graph and a trapezoidal approximation to determine the area bounded by these two quadratic functions
- Using summation notation, write the expression involved in determining this area.
Let's go on to Solids Of Revolution
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