at the lecture of Work, average value, probability(23th lecture) when the professor tried to find the average height of a unit circle( a portion above the x-axis) with y=sin(θ）, he said that the relative weight of lower portion of the upper semi-circle is heavier. But when it comes to y=(1-x)^(1/2)( I mean changing the variable), this does not happen( all relative weight is equal) Why? I cannot understand this point.

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Work, average value, probability
6:30-13:00|dw:1363927655997:dw|

I don't know how to think the 2nd question
can you help me?

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