Let o = 3 and 3 = 7 throughout this question. (i) Using seperation of variables, solve the heat equation au a- U at for a function U(x, t) in the range x E [0, 1] and t ( [0, co) together with the boundary conditions U(x = 0, t) = 0, U(x = 1, t) = 0, and the initial condition Bx U(x, t = 0) = (1-1) B (ii) If the error function is defined as 2 erf( z) = dy , re-express the following integral in terms of the error function or'tax-P dx