Problem 1 (35 points). ул F=3P L=12; P=7; q(x)= Px(x - L) 1. State mathematical formulation of the problem (balance equa

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Problem 1 (35 points). ул F=3P L=12; P=7; q(x)= Px(x - L) 1. State mathematical formulation of the problem (balance equation and boundary conditions) (3 points) 2. Determine the type of boundary conditions (essential or natural) (2 points) 3. Solve the problem by Galerkin method using n₁ = N₁ = x, 12 = N₂ = x² (26 points). 4. Compute the residual r, of the boundary condition specified at x=L (2 points). 5. Determine the residual in balance equation, rb. (2 points) Solution MUST CONTAIN all necessary formulas, equations and all intermediate results. L