Question

Obtain the extremals (if they exist) of the following problem of Lagrange with functional I[x] = ????? (??)² - (x?)² dt, subject to the following auxiliary and boundary conditions: ?? + ?? + ?? = 0, ?? + 2?? = 0, x?(0) = x?(0) = x?(0) = 0, x?(?/2) = -?, x?(?/2) = 3?/2, x?(?/2) = ?/2.

          Obtain the extremals (if they exist) of the following problem of Lagrange with functional
I[x] = ????? (??)² - (x?)² dt,
subject to the following auxiliary and boundary conditions:
?? + ?? + ?? = 0, ?? + 2?? = 0,
x?(0) = x?(0) = x?(0) = 0,
x?(?/2) = -?, x?(?/2) = 3?/2, x?(?/2) = ?/2.

Obtain the extremals (if they exist) of the following problem of Lagrange with functional
I[x] = ????? (??)² - (x?)² dt,
subject to the following auxiliary and boundary conditions:
?? + ?? + ?? = 0, ?? + 2?? = 0,
x?(0) = x?(0) = x?(0) = 0,
x?(?/2) = -?, x?(?/2) = 3?/2, x?(?/2) = ?/2.

Added by -Ngeles P.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Adi S

10/27/2022

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Obtain the extremals (if they exist) of the following problem of Lagrange with functional I[x] = ∫[0,π/2] (ẁ2)^2 - (x2)^2 dt , subject to the following auxiliary and boundary conditions: ẁ1 + ẁ2 + ẁ3 = 0, ẁ1 + 2ẁ3 = 0, x1(0) = x2(0) = x3(0) = 0, x1(π/2) = -π, x2(π/2) = 3π/2, x3(π/2) = π/2