(2) Use the calculus of variations from first principles to extremize the following integral, hence deriving an second order differential equation for y (a) y1/2(1+y)1/2dx To further explain, from first principles implies that you must work through each step of considering variations of y and y, as well as looking at the boundary terms by using integration by parts. (b) Workout the Euler-Lagrange equation for the above integral and confirm it matches your result for the calculus of variations. (c) Workout the Euler-Lagrange equations for the following integrals (i) y2(1+y2)1/2dx (ii) y2(1+y2)2dx