Chapter 5: Applications of Integration
Section 5.7: Centroids
Determine the centroid of the region Rx bounded by fx=x and gx=x2.
The area of region Rx is
A=∫01x−x2 ⅆx = 1/6
Its centroid is given by
x&conjugate0;=11/6∫01x x−x2 ⅆx = 1/2
y&conjugate0;=11/6∫01x2−x22/2 ⅆx = 2/5
Figure 5.7.1(a) Region R and its centroid (black)
The centroid, 1/2,2/5, is the black dot shown in Figure 5.7.1(a).
Calculate A, the area of region Rx
Expression palette: Definite-integral template
Context Panel: Evaluate and Display Inline
Context Panel: Assign to a Name≻A
∫01x−x2 ⅆx = 16→assign to a nameA
1A∫01x x−x2 ⅆx = 12
1A∫01x2−x22/2 ⅆx = 25
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