1. [8 marks] Consider the integral f: x\/ x2 + 1 dx. (a) Using the trapezoidal rule with 5 subintervals, estimate the integral numerically. (b) Find the integral exactly (using calculus and showing the working) and compare this with your numerical result by calculating the absolute value of the error. 2. [8 marks] Find the following integrals. Show all working and give the answer exactly. (a) fie + Dex/3 dx (b) ff x2 111 2x dx 3. [5 marks] Find the average value of the function f (x) : 22a?"2 over x E [0, L]. What happens to the average value as L > on? 4. [9 marks] A lathe is used to make a wooden candlestick so that the radius of the stick at any location is (x is the distance up from the bottom), 33:"2 if0