Chapter 5: Applications of Integration
Section 5.1: Area of a Plane Region
Calculate the plane area bounded by the graph of fx=6+x−x2 and the x-axis.
Recall Example 4.2.1.
Define the function f
Context Panel: Assign Function
fx=6+x−x2→assign as functionf
Determine the x-intercepts of f
Write fx=0 and press the Enter key.
Context Panel: Solve≻Solve
Obtain the area of the given plane region
Expression palette: Definite-integral template
Context Panel: Evaluate and Display Inline
∫−23fx ⅆx = 1256
A graph of the given plane region appears in Figure 5.1.1(a) where the shading indicates the area being calculated.
Figure 5.1.1(a) Plane region bounded by fx=6+x−x2 and the x-axis
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