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Chapter 5: Applications of Integration
Section 5.7: Centroids
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Example 5.7.7
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Determine the centroid of , the parabola .
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Solution
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Define the function
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Context Panel: Assign Function
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Calculate the arc length
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Expression palette: Definite Integral template
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Context Panel: Evaluate and Display Inline
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Context Panel: Assign to a Name≻
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=
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Calculate
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Expression palette: Definite Integral template
Write the formula for .
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Context Panel: Evaluate and Display Inline
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Context Panel: Approximate≻10 (digits)
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=
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Calculate
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Expression palette: Definite Integral template
Write the formula for .
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Context Panel: Evaluate and Display Inline
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Context Panel: Approximate≻10 (digits)
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=
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Figure 5.7.7(a) contains a graph of the parabola , and its centroid (red dot).
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Note that again, the centroid of the curve does not lie on the curve. This was true for the upper half of the circle in Example 5.7.6, but there, so it was pretty obvious that the centroid would not lie on the circle.
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>
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use plots in
module()
local p1,p2;
p1 := plot(x^2, x = 0 .. 1, color = black);
p2 := plot([[.5736270689, .4099802174]], style = point, symbol = solidcircle, symbolsize = 25, color = red);
print(display(p1, p2, scaling = constrained, tickmarks = [3, 3],labels=[x,y]));
end module:
end use:
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Figure 5.7.7(a) Parabola and its centroid
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