4. 5. 6. 7. Supply the details needed to prove the change of variable formula in the special case where C is strictly increasing and differentiable everywhere Show that the function f(x) = x is integrable on [-1,2] and compute its definite integral there. Show that each of the following functions is not integrable on the interval stated: (a) f(x) = 1 for all x irrational and f (x) = 0 if x is rational, on any interval [a,b]. (b) f(x) = 1 for all x irrational and f (x) is undefined if x is rational, on any interval [a,b]. (c) f(x) = 1 for all x 6= 1,1/2,1/3,1/4,... and f(1/n) = cn for some sequence of positive numbers C, C, C ..., on the interval [0,1]. Determine all values of p for which the integrals xdx or xdx