Chapter 5: Applications of Integration
Section 5.7: Centroids
By treating the region Rx in Example 5.7.1 as a region Ry, re-calculate the centroid.
The bounding curve defined by fx=x is now interpreted as x=vy=y.
The bounding curve defined by gx=x2 is now interpreted as x=uy=y.
From Example 5.7.1, A=1/6. Consequently, the centroid is given by
x&conjugate0;=11/6∫01y2−y2/2 ⅆy = 1/2
y&conjugate0;=11/6∫01y y−y ⅆy = 2/5
Calculate A, the area of region R
Expression palette: Definite-integral template
Context Panel: Evaluate and Display Inline
Context Panel: Assign to a Name≻A
∫01y−y ⅆy = 16→assign to a nameA
1A∫01y2−y2/2 ⅆy = 12
1A∫01y y−y ⅆy = 25
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