Weighted Averages: http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-c-average-value-probability-and-numerical-integration/session-61-integrals-and-weighted-averages/MIT18_01SCF10_ex61sol.pdf On Page 2, we find the y-coordinate of the centroid. My question is 1) why do we add up the right and the left side after solving for y 2) wouldn't adding the left and right side yield 2+sqrt(x) and not 2sqrt(x)?

Question

shubhamsrg · Answer

1) they are not ,,they are subtracted,,and its quite obvious why they are subtracted..
take a look at this..
|dw:1350364410794:dw|

the width is always equal to x co-ordinate on right - x co-ordinate on left 
= x -(-x) = 2x in this case..

you may compare this from your case..

2)
1+sqrt(y) - ( 1 -sqrt(y)) = 1 + sqrt y - 1 + sqrt(y) = 2 sqrt(y).. o.O

shubhamsrg · Answer

in 1) , i meant they are no ADDED, but are subtracted *

anonymous · Answer

Got it, thanks @shubhamsrg. :)