Consider the line connecting (x1, y1) (0, 0) and (x2, y2) (1, 1) Show explicitly that the function y(x) x produces a minimum path length by using the varied function y(a, x) x a sin (1 x), use the first few terms in the expansion of the resulting elliptic integral to show the equivalent of Equation...

If we use the varied function Then Thus the total length of the path is dy dx S yax x a ...

Consider the line connecting (x1, y1) = (0, 0) and (x2, y2) = (1, 1). Show explicitly

Question:

Consider the line connecting (x1, y1) = (0, 0) and (x2, y2) = (1, 1). Show explicitly that the function y(x) = x produces a minimum path length by using the varied function y(a, x) = x + a sin π (1 – x), use the first few terms in the expansion of the resulting elliptic integral to show the equivalent of Equation 6.4.