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)/AdA 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)/bunder 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

shubham tomar , 14 Years ago

Grade 12