3. One way to define the natural log, Ina, is as the definite integral dt for x>0; that is dt = ln x. (a) Sketch the graph of 1/t and and approximate In 2 numerically by partitioning the interval [1,2] into 4 equal pieces and computing L4 and R. Write out each sum long-hand, without using a calculator program. (b) Which one of the approximating sums, L or R, do you expect is a better approximation of In 2? Explain. Hint: sketch and compare the areas that represent the errors. (c) Use the Error Bounding formula for L and R, to find an upper bound on the error in the approximations you found in part (a). (d) Suppose we used n = 100 slices instead of 4. What is an upper bound on the error in our approximations? (You don't need to compute L100 or R100!)