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I'm trying to find COM of areas such as : a] area bounded by y=x^2, x= 4 and x axis and, b] half sine wave. Let's try a] first, as there's no symmetry we have to find Xcm and Ycm separately, Xcm = integral( x dA)/A dA area of diff. element. So, ques requires a lot of integration, but as we know COM is just weighted aritmetic mean , can we say Xcm is on the line y = f(c) where, f(x)=x^2 and f(c)= integral (f(x)dx)/b under the limits 0 to b. Let b=4 , then Xcm should be on the line y= 8/3. Am i right? mean value theorem in integrals =integral( f(b)-f(a))/b-a

I'm trying to find COM of areas such as :
a] area bounded by y=x^2, x= 4 and x axis and,
b] half sine wave.
Let's try a] first,
as there's no symmetry we have to find Xcm and Ycm separately, 
Xcm = integral( x dA)/A
dA area of diff. element.
So, ques requires a lot of integration, but as we know COM is just weighted aritmetic mean ,
can we say Xcm is on the line y = f(c)
where, f(x)=x^2 and f(c)= integral (f(x)dx)/b
under the limits 0 to b. Let b=4 , then Xcm should be on the line y= 8/3. Am i right?
mean value theorem in integrals 


=integral( f(b)-f(a))/b-a

Grade:12

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