Solve all the problems:

For the following problem, approximate the integral using the midpoint rule, trapezoidal rule, and Simpson's rule using 4 subintervals, rounding to three decimals. 7) If esin (x2) dx For the following problem, evaluate the integral, if possible. 8) I100 3% dx, for what values of n does this integral converge of diverge? For the following problem, consider the gamma function given by ['(a) = If e'yy'I1dy 9) Show that I'(a) = (a 1)F(a 1)