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mahrap

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- Thread starter mahrap
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In summary, To calculate the average height above the x-axis of a point in the region 0 <= x <= 1 , 0 <= y <= x^2, you will need to integrate y over the region and then divide by the area of the region. This can be set up as a double integral of y. The height in this case refers to the distance of a point (x,y) to the x-axis.

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mahrap

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Dick

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mahrap said:

I expect height means y. So you want to integrate y over the region then divide by the area of the region. Set it up as a double integral of y.

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mahrap

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Dick said:I expect height means y. So you want to integrate y over the region then divide by the area of the region. Set it up as a double integral of y.

Why would the height be y though? That's what i don't understand

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Dick

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mahrap said:Why would the height be y though? That's what i don't understand

y is the distance of a point (x,y) to the x-axis. They are just calling that 'height'.

The formula for the average value of the x-coordinate in a semicircle is simply the radius of the semicircle divided by 2. This is because the x-coordinate varies from -r to r in a semicircle, and the average of this range is 0.

The formula for the average value of the y-coordinate in a semicircle is given by (2r/π), where r is the radius of the semicircle. This is because the y-coordinate follows a sine curve in a semicircle, and the average value of a sine curve over one period is 2/π.

No, the average value of the x-coordinate and y-coordinate in a semicircle will always be different. This is because the x-coordinate varies over a range of values from -r to r, while the y-coordinate follows a sine curve and varies from 0 to r.

As the radius of the semicircle increases, the average value of the x-coordinate will remain the same (r/2), but the average value of the y-coordinate will increase. This is because the larger the radius, the longer the sine curve and the larger the average value of the curve.

If the semicircle is rotated or translated, the average value of the x-coordinate and y-coordinate will remain the same. This is because the rotation or translation does not change the overall shape or position of the semicircle, and therefore does not affect the average values of the coordinates.

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