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How do you find the centroid of the quarter circle of radius 1 with center at the origin lying in the first quadrant?

Answer 1

Non-Calculus Solution:

Observation 1:
The centroid must lie along the line #y = x# (otherwise the straight line running through #(0,0)# and the centroid would be to "heavy" on one side).

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Answer 2

Aurora Alvarado

To find the centroid of the quarter circle of radius 1 lying in the first quadrant, you can use the formulas for the centroid of a region. For a quarter circle, the centroid lies along the axis of symmetry, which in this case coincides with the y-axis.

The x-coordinate of the centroid (¯x) for a quarter circle with radius r is given by the formula:

¯x = (4r) / (3π)

In this case, r = 1, so:

¯x = (4(1)) / (3π) = 4 / (3π)

Since the centroid lies along the y-axis, the x-coordinate is 0.

Therefore, the centroid of the quarter circle of radius 1 lying in the first quadrant is at the point (0, 4 / (3π)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.