Question

Find the exact coordinates of the centroid of the region bounded by y = 2x + 3, y = x^2

Answer 1

do you know the formulla directly ?

Answer 2

well leme tell then,,
from the graph, 2x+3 will lie over x^2 in the bounded reigon..

now, let f(x) = 2x+3 and g(x) = x^2
let these 2 intersect at a and b (a < b) ( both are x-co-ordinates)

let f(x) + g(x) =m
and f(x) -g(x) =n
also, integral (n dx) = A=area ,ofcorse !

now, there;s this direct formulla, which doesnt have a very tough derivation actually..

x co-ordinate is = integral (x*n dx) / A
y cor-ordinate is =integral (n*m dx) /2A

note: limits of all integrals above is from a to b.

hope this helps..

Answer 3

thanks , what next

Answer 4

substitute in the values..i guess??