Question

Find the exact coordinates of the centroid for the region bounded by the curves y=x,y=x, y=1/x,y=1/x, y=0,y=0, and x=2

Answer 1

i) The x coordinate of the centroid is given by: (1/A)∫{x*f(x)}dx in [x = a to b]

ii) And y coordinated of the centroid is given by: (1/A)∫[f(x)]² dx in [x = a to b]

iii) And A is the area which is given by ∫f(x) dx in [x =a to b]

iv) Here, f(x) = 1/x; a = 1 and b = 2

Substituting these and evaluating we get the coordinates as: ( 1/ln|2|, 1/4ln|2| )