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QUESTION 1 To compute the area below the curve f(x), above the x-axis, from x a...
Use the rectangles to approximate the area of the region. f(x) = -x + 11 [1, 11] y 10 8 6 2 2 4 6 8 10 10 Х Give the exact area obtained using a definite integral. 10 x Need Help? Read it Watch It Talk to a Tutor Use the rectangles to approximate the area of the region. (Round your answer to three decimal places.) f(x) = 25 – x2, (-5,5) y 23 20 15 10 -6 2...
19. Given the graph of f(x) below. Find the area between f(x) and the x-axis on ](-2, 8]then determine if the area is equivalent to the definite integral over that same region? Area = a. b. Is the area equivalent to the definite integral? If not, determine the definite integral of the function from (-2, 8]. -2
Estimate the area of the region bounded by the graph of f(x)-x + 2 and the x-axis on [0,4] in the following ways a. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a midpoint Riemann sum· illustrate the solution geometrically. C. Divide [04] into n = 4 subintervals and...
Mth 229, Calculus Computer Laboratbi The length of a curve defined by the graph of fx) from x-a to x b is givell U definite integral +dx shown below. Find the length of the sine curve from 0 to 2π as we can see that 7.44 is a Using the sum of the lengths of the selected sides of the upper bound for this of the selected sides of the three triangles Using the lengths lower bound for this arc...
5. (12 pts.) Consider the region bounded by f(x) 4-2x and the x-axis on interval [-1, 4] Follow the steps to state the right Riemann Sum of the function f with n equal-length subintervals on [-, 4] (5 pts.) a. Xk= f(xa) (Substitute x into f and simplify.) Complete the right Riemann Sum (do not evaluate or simplify): -2 b. (1 pt.) lim R calculates NET AREA or TOTAL AREA. (Circle your choice.) Using the graph, shade the region bounded...
Construct and simplify a sum approximating the area above the x-axis and under the curve y = x2 between x = 0 and x = 3 by using n rectangles having equal widths and tops lying above or on the curve. Find the actual area as a suitable limit ОА. 9(n-1)(2n-1) area = 9 square units 2n2 B 9(n + 1) 2n area = 9 square units ос. 3(n-1)(2n-1) n2 area = 6 square units OD 3(n + 1)(2n +...
e (10 pts.) Approximate the area between the curve f(x) and x 3, by the following methods: and the x-axis, between x 0 a. Using 6 rectangles (n 6), and the Midpoint Rule. b. Using 6 rectangles, and left endpoints. c. Using 6 rectangles, and right endpoints. d. Find the average of your answers for parts (b) and (c). e. Compute the percent error for you answers in parts (a) and (d), using the following: - exact answer I calculated...
answer 1-4 6.3.14 Compute the area of the shaded region that is shown in the graph below. The area of the shaded region is (Simplify your answer.) a y = - 2x - 1)(x-6) Q ni core: 0 of 1 pt 1.3.11 Fill in both of the answer boxes to complete the integral Set up the definite integral that gives the area of the shaded region of the graph below. Do not evaluate the integral JO Question Use a Riemann...
can you please solve all the questions 4 a) Find fx) dx using the Left-hand Sum. ONote ar is not 2 1 consta) fx) 5.75 9.5 12 14 b) Sketch the rectangles used to evaluste the definite integral in a) 10 Evaluate the definite integral using the Right-hand Sum e) fn The regions A. B, and C in the figure above are bounded by the graph of the function fand the a-axis If the area of each 5. region is...
Use a definite Integral to find the area of the following region bounded by the given curve, the x-axis, and the given lines in each case, first sketch the region. Watch out for areas of regions that are below the x-axis yox?x-2.x=1 Choose the correct graph below. OA Oc OD OB 5 The total area of the region is (Type an integer or a fraction