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

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Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.

y = 2x,  y = 0,   x =1
asked Jan 29, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The functions are , and

The region bounded by the curves :

Observe the figure:

The area of the region bounded by the curves is A  = 1.

Step 2:

The centroid of the region is .

.

Substitute and in above equation.

Step 3:

.

Substitute and in above equation.

.

The centroid of the region is

Step 4 :

The graph of the functions image and the centroid image :

image

Solution :

The centroid of the region is

The graph of the functions image and the centroid image :

image

answered Feb 2, 2015 by Thomas Apprentice
edited Feb 2, 2015 by Thomas

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