Let a < b and let f(x) be a continuously differentiable function on theinterval [a, b] with f(x) > 0 for all x = [a, b].Let A > 0, B > 0 be constants.S[y] =is given byy(x)=[* dx ƒ(x)√1+y¹², _y(a) = A₁ y(b) = B,A,aA+B1² ddw1√f(w)²- ß²where is a constant satisfyingbB-A= B 3 [ºadw1√f (w)² - 82the stationary pathgives a weak local minimum of the functional S[y].Using the Jacobi equation,

Given functional is where is continuously differentiable function on the interval So to get optimum…

Let a < b and let f(x) be a continuously differentiable function on the interval [a, b] with f(x) > 0 for all x = [a, b]. Let A > 0, B > 0 be constants. S[y] = da [* dx f(x)}√/1+ y^², _y(a) = A, y(b) = B, a is given by y(x) = rx [² d A+B B-A= B dw where is a constant satisfying b 35° a 1 √f(w)² - 3² dw 1 √f (w)² — B²*

Let a < b and let f(x) be a continuously differentiable function on the interval [a, b] with f(x) > 0 for all x = [a, b]. Let A > 0, B > 0 be constants. S[y] = da [* dx f(x)}√/1+ y^², _y(a) = A, y(b) = B, a is given by y(x) = rx [² d A+B B-A= B dw where is a constant satisfying b 35° a 1 √f(w)² - 3² dw 1 √f (w)² — B²*

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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