Chapter 5: Applications of Integration
Section 5.1: Area of a Plane Region
Calculate the plane area bounded by the graph of fx=x3−7 x2+5 x+4 and the x-axis.
Recall Example 4.2.5. where the area of a slightly different plane region was found. The shaded region in Figure 5.1.2(a) is bounded by y=fx and y=0. However, part of the region lies below the x-axis, the integration must be over two contiguous intervals, a,b and b,c, where a,b,c are the x-intercepts of f.
Figure 5.1.2(a) Region bounded by fx and thex-axis
Define the function f
Context Panel: Assign Function
fx=x3−7 x2+5 x+4→assign as functionf
Obtain the x-intercepts a,b,c
Write the equation fx=0 and press the Enter key.
Context Panel: Solve≻Numerically Solve
Context Panel: Conversions: To List
Context Panel: Assign to a Name≻x
→assign to a name
Calculate the area of the region bounded by y=fx and y=0
Expression palette: Definite-integral template
Context Panel: Evaluate and Display Inline
∫X1X2fx ⅆx−∫X2X3fx ⅆx = 77.25663235
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