1. Solve the problem given below using Galerkin's method and the four piecewise linear trial functions shown below. (total 10 pts) d'u du 0Sx u(O)-0, u(1)-1 (x) 2(x) 1/3 2/3 0 1/3 2/3 , (x) , (x) 1/3 213 0 13 2/3 1) Derive the weak formulation (2 pts) Given the following trial function ux)=a.1(x)-a,, (x)-a,4, (x)-a,4 4(x). determine a and a using the essential boundary conditions. (1 pt) Determine the weighted residual integration for weight function w2 (r). For Galerkin's method, w, (x 2) 3) on(x) 4) Determine the weighted residual integration for weight function w (x). For Galerkins method, w,(x)-ou(x)-, (x). (2pts) 5) Acquire the approximate solution u(x) by determining all coefficients ai (i = 1 to 4) (2 pts) 6) What is the approximate solution at x- 0.7? (1 pt) 1. Solve the problem given below using Galerkin's method and the four piecewise linear trial functions shown below. (total 10 pts) d'u du 0Sx u(O)-0, u(1)-1 (x) 2(x) 1/3 2/3 0 1/3 2/3 , (x) , (x) 1/3 213 0 13 2/3 1) Derive the weak formulation (2 pts) Given the following trial function ux)=a.1(x)-a,, (x)-a,4, (x)-a,4 4(x). determine a and a using the essential boundary conditions. (1 pt) Determine the weighted residual integration for weight function w2 (r). For Galerkin's method, w, (x 2) 3) on(x) 4) Determine the weighted residual integration for weight function w (x). For Galerkins method, w,(x)-ou(x)-, (x). (2pts) 5) Acquire the approximate solution u(x) by determining all coefficients ai (i = 1 to 4) (2 pts) 6) What is the approximate solution at x- 0.7? (1 pt)