When dy/dx = (x -6)1/2, what does y equal?

Considering that the given derivative is:

 dy
= (x - 6)^ (1/2) ,
 dx

y is the function whose derivative is (x - 6)^ (1/2).

Given that the derivative of (x - 6) ^ (3/2) is (3/2)* (x - 6)^ (1/2), you have that the function searched is y = (2/3) ( x - 6) ^ (3/2) plus a constant.

You can prove that dy / dx is (2/3)*(3/2) (x - 6) ^ (3/2) = (x - 6)^ (1/2).

y = (2/3) (x - 6)^(3/2).+ constant