$2 Consider the function f(:r) = 7? + 4. 2 2 In this problem you will calculate / (i z? + 4) dx by using the denition 0 The summation inside the brackets is Rn which is the Riemann sum where the sample points are chosen to be the righthand endpoints of each subinterval. 2 Calculate RH for f (m) = 7% + 4 on the interval [0, 2] and write your answer as a function ofn without any summation signs. You will need the summation Formulas \" n(n+1) n2+n 1 2 =:'=7= + +3+ +72 2 2 2 , {:1 " +1)(2n+1) 2n3+3n2+n 12 22 32 1 2 _ -2 _ n(n _ + + + n E z 6 6 , 21 Show hint Consider the integral given by (1 -x') dx Using the following definition of the integral f(x)dx = lim >f(x;) Ax a n-+00 i=1 where x; are right hand endpoints. (a) Determine Ax and xi. Ax = Ci (b) Using the definition mentioned above, evaluate the integral. Value of integral