Consider the function f(ac) = - 202 + 4. 3 ac 2 In this problem you will calculate 3 + 4 ) dx by using the definition f(xx) da = lim The summation inside the brackets is Rn which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval. Calculate Rn for f(a) = _ 2- 3 - + 4 on the interval [0, 2] and write your answer as a function of n without any summation signs. You will need the summation formulas n(n + 1) n- tn 1 + 2 + 3 + . . . + n = > i= i= 1 2 2 12 + 22 + 32 + ... + n' = ) i2 = n(n + 1) (2n + 1) 2n' + 3n2 + n i= 1 6 6 Rn = lim Rn = n -tooConsider the integral given by (1-x2) da Using the following definition of the integral .b f(x) da = lim a n-+00 i=1 where xi are right hand endpoints. (a) Determine Ax and xi. Ax = C = (b) Using the definition mentioned above, evaluate the integral. Value of integral