For a linearly elastic material, the stress T (x) is given as where u(x) is the displacement of the.

For a linearly elastic material, the stress T (x) is given as where u(x) is the displacement of the material and E is a positive constant known as the Young’s modulus. The question considered here is, how to determine u from measurements of T , as given in Table 6.10. (a) Show that In the following you can assume that u(0) = 0 and E = 4. (b) Use the trapezoidal rule to find the value of u(x) at x = 1/4, 1/2, 3/4, 1. (c) Use the composite midpoint rule to calculate u(1). (d) Use the composite Simpson rule to calculate u(1). (e) Use Romberg integration with the composite trapezoidal rule to calculate u(1).