1. (2pts) Suppose f(x) = ax +b where a and b are real numbers. Consider the definite integral f(x)dx . Suppose we use the Midpoint rule to approximate this definite integral with n = 2. Prove that the approximation we obtain is equal to f(x)dx . 2. (3pts) We define the modified Gabriel's horn as the solid obtained by rotating the region bounded by y = and y =0 on the interval 1, co) about the x-axis. Find whether or not the surface area of the modified Gabriel's horn is finite (if it is finite you do not have to find the exact surface area). Justify your answer (Hint: Use the comparison theorem, and the fact that for positive real numbers a and b Vatbsva+vb)