UMUC MATH 140, FALL 2017 QUIZ 5 SOLUTION KOBI SNITZ (1) Let a1 be the ith digit of the expansion of so that a1 = 3 and a2 = 1 etc. evaluate the expression 11 X ai1 ai i=2 (2) Use a Riemann sum with 5 sub-intervals to approximate the area under the curve of f (x) = x2 + 2 between 3 and 7. (3) Calculate an upper sum and a lower sum for the partition in question (2). [hint: you will need to use what you know about derivatives to find the maximum and minimum of each sub-interval] (4) Evaluate the integral Z 7 x2 + 2 dx 3 If all goes well it should be close to the answers you got in questions (1)-(3) (5) Evaluate the integral Z 10 cos(x + 1) dx 5 1