determine the co-ordinate of the poin of intersection of the curves y=x*x and y*y=8x. sketch the two curves and find the area enclosed by the two curves.

Answer 1

y = x^2 = sqrt(8x)
x^4 = 8x
(x^3 - 8)*x = 0
x = 0 or 2

For the area between the curves, integrate
(8x)^(1/2) - x^2
from 0 to 2.

sqrt8*2^(3/2)/(3/2) - (2^3)/3
= 16/3 - 8/3 = 8/3