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In Figure 4.2.5(a), the areas of regions , and , shaded in yellow, must be calculated separately because regions and are below the -axis.
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Thus, it is imperative to find the intercepts and .
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Unfortunately, exact representations of these intercepts are large and cumbersome expressions. These intercepts will be approximated numerically.
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Once the values of and have been determined, the desired area would be given by
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Figure 4.2.5(a) Graph of
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Table 4.2.5(a) lists the exact values of and , obtained by simplifying the results returned by Maple's solve command.
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Table 4.2.5(a) Exact values of the intercepts and
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Numeric approximations of and are found below, and these values are used in the appropriate definite integrals to calculate the sum of the areas in regions , and in Figure 4.2.5(a).
Define the function
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Control-drag
Context Panel: Assign Function
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Obtain numeric values for and
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Write and press the Enter key.
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Context Panel: Solve≻Numerically Solve
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Context Panel: Conversions≻To List
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Context Panel: Assign to a Name≻
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Calculate the area
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Write the sum of definite integrals determining the area. Use for and for .
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Context Panel: Evaluate and Display Inline
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=
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