Question

Sketch the region bounded by the curves, and visually estimate the location of the centroid. y = 4x, y = 0, x = 1

Answer 1

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Answer 2

Given:

The curves y  = 4x , y = 0 and x =1 .

To Find:

Sketch the region bounded by the curves, and visually estimate the location of the centroid.

Solution:

Given curves are y = 4x , y = 0 , and x =1 .

These curves intersect at 3 points.

• y =4x and y =0  intersect at (0,0).
• y =4x and x =1 intersect at (1,4).
• y =0 and x =1 intersect at (1,0).

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

• X = (0 + 1 + 1 )/3 = 2/3
• Y = (0+4+0)/3 = 4/3

Therefore the coordinates of centroid are ( 2/3 , 4/3).