Posted by tia on Sunday, April 6, 2008 at 11:22pm.
could some body please check this for me?
1. find the exact coordinates of the centroid of the region bounded by yx^2, the x axis, the y axis, and the line x=1?
I said the answer was ((3/4), (3/10))
2. Find the exact coordinates of the centroid of the region to the right of the y axis between y=2e^(2x) and the x axis. Note this region is unbounded but has a finite area.
I said the answer was ((1/2), (1/2))
THANK YOU

calculus  drwls, Monday, April 7, 2008 at 12:27am
1. Do you mean y = x^2? You wrote yx^2. That is not a curve.
If you mean y = x^2, the areaweighted mean value of y is
[integral of y(y/2)dx] divided by 1/3
x = 0 to 1
= 3/10
The areaweighted mean value of x is
integral of y*x dx divided by 1/3
x = 0 to 1
= integral of x^3 dx divided by 1/3
x = 0 to 1
= 3/4
The division by 1/3 is normalizing by the area of the region. I agree with your answers. If you followed the same procedure for problem 2, your answers to that one are also correct.
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