Chapter 5: Applications of Integration
Section 5.7: Centroids
Determine the centroid of C, the upper half of the unit circle whose center is at the origin.
The curve C can be defined by the equation y=1−x2, x∈−1,1, so S=π,
=1π∫−111−x2 dx1− x2
Clearly, since y0=1≠2/π, the centroid does not fall on the curve itself.
Define the function y
Context Panel: Assign Function
yx=1−x2→assign as functiony
Calculate the coordinates of the centroid
Write the integral for x&conjugate0;.
Context Panel: Evaluate and Display Inline
1π∫−11x1+y′x2 ⅆx = 0
Write the integral for y&conjugate0;.
1π∫−11yx1+y′x2 ⅆx = 2π
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