To find: The total area of the region between the given curve and the x -axis.
Answer to Problem 44E
The total area of the region between the curve and the x -axis is 8
Explanation of Solution
Given Information:
A given curve
Formula used:
To evaluate the area under the graph with axis, for a given interval
1) Divide the given interval into sub-intervals such that its limits are the points at which the curve meets the x -axis.
2) Integrate the given curve over these limits.
3) Obtain the sum of absolute value of integrals to get the total area of the region between the curve and x -axis.
Calculation The graph of the given function
Here, the blue region defines the interval over which the function is to be considered. From the graph, it can be seen that, the curve meets the x -axis at points -2, 0 and 2. Thus, the sub- intervals to be considered are [-2, 0] and [0, 2].
Considering the first interval [-2, 0], the integral of the given function is,
Now, consider the interval [0, 2], integral over which is,
Adding the absolute values of the integral, the total area of the region with the x-axis is given by,
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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