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I will take all your effort to solve this problem and will give you a good rate!!!

Please show all the calculations in detail!

Also, please do not copied and pasted answers from another website (Especially c_h_e_g_g)

(2) Among all the curves y(:::) joining two given points (3:1, yl) and (1:2, yg), nd the one that generates the minimum surface area when rotated about the x-axis. Recall that the area of the surface of revolution generated is I2 A : QH/yx/l + (y'Fdn: 171 Derive the Euler-Lagrange equation for this functional and show that the solution is a: + (:21 Cl y(:r) : (:1 cosh [ Evaluate the constants C] and 02 for the case where (931,3;1) = (0, 1) and ($2.. yz) : (1.. 10) and plot the resulting curve. The integrand of a functional can depend upon derivatives of higher order, for example second order as 1'2 I:/f(:r._y._y'._y")d:r. 1'1 Derive the Euler-Lagrange equation that renders this functional stationary with respect to weak variations in 3,:(17). Specify all possible boundary conditions