Problem 1 [4 pts] Consider the region R below the curve y = 2x – 1?...
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...
B Consider the shaded region bounded by y=x2 – 4 and y= 3x + 6 (see above). Note that the r-axis and y-axis are not drawn to the same scale. (a) Find the coordinates of the points A, B, and C. Remember to show all work. (b) Set up but do not evaluate an integral (or integrals) in terms of r that represent(s) the area of the region. That is, your final answer should be a definite integral (or integrals)....
Consider a solid whose base is the region bounded by the curves y = (−x^2) + 3 and y = 2x − 5, with cross-sections perpendicular to the y-axis that are squares. a) Sketch the base of this solid. b) Find a Riemann sum which approximates the volume of this solid. c) Write a definite integral that calculates this volume precisely. (Do not need to calculate the integral)
Please show full workings for both parts of the answer because I keep getting the answer wrong. Thumbs up will be given to the workings with correct answers! 7. Set up (do not solve) a definite integral that would give the area of the region under the graph of y = In x, above the x-axis, between the vertical lines x = 1 and x = e. Sketch the graph. You don't need to express with the Riemann sum definition...
cannot figure out how to write the integrals for this problem #2 1. If glx) -2x and fx) - , find the area of the region enclosed by the two graphs. Show a work for full credit. (4 pts) 2. A:12-80% 3 3 2 Let fix)-. Let R be the region in the first quadrant bounded by the gruph of y - f(x) and the vertical line x # l, as shown in the figure above. (a) Write but do...
6. (6 pts) (x)-4-2x on [0,4] a. b. Sketch the function on the given interval. 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 c. Use the sketch in part (a) to show which intervals of [a,b] make positive and negative contributions to the net area. (4 pts Use geometry (not Riemann sums) to evaluate the following definite integrals Sketch a graph of...
Instructions: Show all your work for FULL credit. Calculators are NOL final answer. Neatness is highly appreciated. 1. A region R, bounded by y 2x, y 6-x, and x-axis, is rotated around the y-axis. Sketch the region R, in the box a) 15 strip/slice you will use to find the volume of the solid of revolution. b) Write the definite integral that gives a X the volume of the solid of revolution. (DO NOT evaluate the integral.) Find the circumference...
and the r-axis. 5. Consider the region S bounded by r 1, r = 5, y (a) Use four rectangles and a Riemann sum to approximate the area of the region S. Sketch the region S and the rectangles and indicate your rectangles overestimate or underestimate the area of S. (b) Find an expression for the area of the region S as a limit. Do not evaluate the limit. and the r-axis. 5. Consider the region S bounded by r...
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...
Let C be the portion of the curve rve y = x3 + 3x – 1 between the points (1, 3) and (2, 13). (a) Write down a definite integral for the arclength of C. Do not evaluate the integral. (b) Write down a definite integral for the surface area of the surface of revolution obtained by revolving Cabout the x-axis. Do not evaluate the integral. (c) Write down a definite integral for the surface area of the surface of...