The following function is positive and negative on the given interval. 31: f(x) = sin 2x; [0,7] 3. Sketch the function on the given interval. b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n = 4. 31: c. Use the sketch in part (a) to show which intervals of [0,7] make positive and negative contributions to the net area. a. Choose the correct answer below. {:2- A. {jz- B. {:2- C. .3. D. A A A 2 y Q 2 y Q 2 y Q 2 y Q 1 1 1 1 x Q x Q x Q x Q 0 n a 2 > o n a" 2 > 0 1: a 2 > o n 31: 2 > 7|: 7|: 1[ 7|: TI 1[ .1 2' _1 2' _1 \\g/ 2' _1_ % 2' 2 D 2 D 2 D 2 D -2 -2 -2 -2 b. Use a calculator to approximate the area. The net area, approximated using the left Riemann sum with n = 4, is (Do not round until the nal answer. Then round to three decimal places as needed.) Use a calculator to approximate the area. The net area, approximated using the right Riemann sum with n = 4, is (Do not round until the nal answer. Then round to three decimal places as needed.) Use a calculator to approximate the area. The net area, approximated using the midpoint Riemann sum with n =4, is (Do not round until the nal answer. Then round to three decimal places as needed.) 31: c. Which intervals of [0,7] make positive and negative contributions to the net area? .-. . . . it 31: A. Positive on 0,5 ,negatlve on 5,4 __ 1c 31: . 1: B. Posmve on 2, 4 ,negatlve on 0, 2 4:3. c_ Positive on [Ont]; negative on [1:211] 8 8 Consider two functions f and g on [3,8] such that f(x)dx = 11, g(x)dx = 5, f(x)dx =7, and g(x)dx =2. Evaluate the following integrals. a. 6f(x)dx = (Simplify your answer.) 8 b. (f(x) - 9(x))dx = (Simplify your answer.) 3 c. (f(x)-9(x)dx =(Simplify your answer.) 3 8 d. (9(x)-f(x)dx = (Simplify your answer.) 6 e. 8g(x)dx = (Simplify your answer.) 6 w F. 4f (x)dx = (Simplify your answer.) 6Evaluate the following integral using the Fundamental Theorem of Calculus. Discuss whether your result is consistent with the figure. [ (x2- 3x +5) dx 4- 2- -0.5 0 5 [ (x2 - 3x + 5) dx = [ Is your result consistent with the figure? O A. No, because the definite integral is positive and the graph of f lies below the x-axis. O B. No, because the definite integral is negative and the graph of flies above the x-axis. O C. Yes, because the definite integral is positive and the graph of flies above the x-axis. O D. Yes, because the definite integral is negative and the graph of f lies below the x-axis.X The graph of f is given in the figure to the right. Let A(x) = f(t) dt and evaluate A(4), A(7), A(10), and A(12). 16 of circle radius 4 A(4) = (Type an exact answer in terms of It.) A(7) = (Type an exact answer in terms of T.) A(10) = (Type an exact answer in terms of J.) A(12) = (Type an exact answer in terms of T.)Find parametric equations of an ellipse centered at the origin with major axis of length 18 on the x-axis and minor axis of length 4 on the y-axis, generated counterclockwise. Graph the ellipse and nd a description in terms of x and y. Find a set of parametric equations. Assume the ellipse starts at its rightmost point. x= ,y= ;OSt521: Graph the ellipse. Choose the correct graph below. OA. OB. Find a description in terms ofx and y. xzyz +=1 |