The following function is positive and negative on the given interval. f(x) = 5 - 5x2; [0,4] a. Sketch the function on the given interval. b. Approximate the net area bounded by the graph offend the x-axis on the interval using a left, right, and midpoint Riemann sum with n = 4. c. Use the sketch in part (a) to show which intervals of [0,4] make positive and negative contributions to the net area. a. Choose the correct answer below. V y Ay Ay 6' 9: 6' $2 6" X 60 O > x Q 48 Q 12 Q 36 -24 m 33 x m 32 m 13 ' $3 :24 f 1 (f {f :84 b. The net area, approximated using the left Riemann sum, is - 50 . The net area, approximated using the right Riemann sum, is Consider the following limit of Riemann sums of a function f on [a,b]. Identify f and express the limit as a definite integral. lim XK AXK; [2,8] 4-0 k = 1 . . . The limit, expressed as a definite integral, isConsider the following limit of Riemann sums of a function f on [a,b]. Identify f and express the limit as a definite integral. lim _ xx Inxx AXK; [2,3] 4-0 K = 1 . . . The limit, expressed as a definite integral, isUse geometry (not Riemann sums) to evaluate the following definite integral. Sketch a graph of the integrand, show the region in question, and interpret your results. A f ( x ) dx , where f ( x ) = 5 if xs 2 3x - 1 if x > 2 . . . Sketch a graph of the integrand, and then shade the region in question. Choose the correct graph below. O A. O B. O C. 13- 13- X XThe figure to the right shows the area of regions bounded by the graph of f and the X-axis. Evaluate the following integral. y = f(x) | f( x ) dx 14 11 0 O 6 . . . f ( x )dx = (Type an integer or a simplified fraction.) 0The figure to the right shows four regions bounded by the graph of y = x sin x: R1 , R2, R3, and Arca = 1 Arca = 7 + 1 R4, whose areas are 1, I - 1, it + 1, and 2x - 1, respectively. Use this information to evaluate the y = x sin x following integral. R1 R2 3x/2 R3 RA x sin x dx Arca = 1 - Area = 2w - 1 . . . 3T/2 - x sin x dx = (Type an exact answer, using it as needed.) OUse the value of the first integral I to evaluate the two given integrals. 1= (x3 - 5x) dx = -- -ACO 0 a. (30x - 6x3) dx b. (5 x - x 3 ) dx 0 a. (30x -6x3) dx = (Simplify your answer.) 09 CO 6 Consider two functions f and g on [3,9] such that f(x)dx = 15, g(x)dx =7, f(x)dx =8, and g(x)dx =4. Evaluate the following integrals. 3 6 3 . . . a. 9f(x)dx = (Simplify your answer.)Graph the following function. Then use geometry (not Riemann sums) to nd the area and net area of the region described. The region between the graph of y = 2x - 2 and the x-axis from 0 s x s 5 Select the correct graph of y = 2x - 2 below. Q x Q 13' The area of the region is El square units. (Type an integer or a simplied fraction.)