Concept explainers
To describe: The process for finding the area between two curves.
Explanation of Solution
The process for finding the area between two curves:
Suppose
To find the area of the region
That is,
Suppose
To find the area of the region between the curves defined by
of the interval
For each index
and height,
equal to the vertical distance between the two curves at
Refer to the approximating rectangle as a vertical strip which is shown in Figure 6.3.
The representative rectangle has area
And the total area between the curves
Increase the number of subdivision points in the partition
Thus, the region between the two curves has area
This is the integral of the function
Using all the above observations, the area between the two curves can be defined as,
If
Conclusion: Thus, the area between two curves is
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Chapter 6 Solutions
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