UMUC MATH, FALL 2016 QUIZ 1, SOLUTION KOBI SNITZ (1) Let f (x) = 3x2 2x and let 2 4 6 2n 2 Pn = {1, 1 + , 1 + , 1 + , . . . 1 + , 3} n n n n Write the lower and upper Riemann sums LSpn , U Spn for this function for the partition in sigma notation. [hint: use your knowledge of functions to locate the minimum and maximum values in each interval]. Find an n such that the difference U Spn LSpn < 0.5. (2) find the anti derivative of f (x) = x cos(x2 ) (3) evaluate the following definite integral Z 7 exp(2x 3) dx A= 3 (4) Let f (x) = 3x2 and let L be the line 2x + 1. Calculate the area which lies between the line L and the graph of f . 1