Question

Sketch the region bounded by the curves, and visually estimate the location of the centroid. y = 5/x, y = 0, x = 1, x = 2

Answer 1

The coordinates of centroid bounded by the curves is (5/3, 7.5/3).

In this question,

The curves are y = 5/x, y = 0, x = 1, x = 2

These curves are plotted in the graph as shown below.

From the graph, these curves intersect at 3 points. They are

• The curves y = 5/x and x = 1 intersects at (1,5)
• The curves y = 5/x and x = 2 intersects at (2,2.5)
• The curves y = 0 and x = 2 intersects at (2,0)

The centroid of a planar geometric region (X,Y) is the arithmetic mean of all the points contained in the region.

Let X be the x coordinate of the centroid and Y be the y coordinate of the centroid.

Then, X = (1 + 2 + 2)/3

⇒ X = 5/3

Y = (5 + 2.5 + 0)/3

⇒ Y = 7.5/3

Thus the coordinates of centroid bounded by the curves is (5/3, 7.5/3).

Learn more about coordinates of centroid here

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