Chapter 5: Applications of Integration
Section 5.1: Area of a Plane Region
Example 5.1.2
Calculate the plane area bounded by the graph of and the -axis.
Solution
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 and . However, part of the region lies below the -axis, the integration must be over two contiguous intervals, and , where are the -intercepts of .
module () local f,q,p1,p2,p3,p; f:=x^3-7*x^2+5*x+4; q:=fsolve(f,x,complex); p1:=plot(f,x=q[1]..q[3],labels=[x,y],color=black,filled=[color=red,transparency=.7],thickness=2); p2:=plots:-textplot({[6,.7,typeset(c)],[-.3,.7,typeset(a)],[1.5,.7,typeset(b)]},font=[default,12]); p3:=plot([[q[1],0],[q[3],0]],style=line,color=black,thickness=2); p:=plots:-display(p1,p2,p3); print(p); end module:
Figure 5.1.2(a) Region bounded by and the-axis
Define the function
Control-drag Context Panel: Assign Function
Obtain the -intercepts
Write the equation and press the Enter key.
Context Panel: Solve≻Numerically Solve
Context Panel: Conversions: To List
Context Panel: Assign to a Name≻
Calculate the area of the region bounded by and
Expression palette: Definite-integral template
Context Panel: Evaluate and Display Inline
=
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