Unit 6 Study Guide- The Definite Integral 1 . Base your answer on x 0 1 2 3 4 S(x) 0 1.2 4.3 6.5 1 For the function whose values are given in the table above. approximate / f(x)dx using a Riemann Sum with a midpoint rule of two intervals. a. 12 b. 12.5 c. 13 d. 15.4 e. 16.7 2. A) A rainstorm hit Portland, Maine, in October 1996, resulting in record rainfall. The rainfall rate R(t) on October 21 is recorded, in inches per hour, in the following table, where t is the number of hours since midnight. Compute the total rainfall during this 24- hour period using a right and a left approximation with 5 subdivisions. t 0 3 5 10 16 24 R(1) 0.2 0.1 0.4 1.0 0.6 0.25 B) Using the table above compute forR(t) dt using trapezoidal approximation wit 5 subdivisions. 3. X 2 5 6 f(x) -1 1 2 | 6 12 The table above shows selected values of a function f(x). Use a right-hand approximation with the subintervals defined by the values in the table to approximate the area under the curve of f (x) on the interval [2, 6]. (A) 13 (B) 17.5 (C) 26 (D 9 (E) None of the above 4. Base your answer on it f(x)dx - -Gand 'f(x)dx - 4. then / f(x)dx = 3. -10 b. -2 c 2 d. e. 105. Given S, f(x)dx = -5, S, f(x)dx = 6, S2 g(x)dx = 6. Find each of the following. a. Sof (x) dx = b. S 3f (x ) dx = c. Sof (x) dx = d. SoIf (x) + g(x)]dx = e. S 49(x) dx = 6. N O The graph of a piecewise linear function f, for -1