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6. [10 points] Consider the function f(x) = 2 + cose over the interval (1,6), where...
Define R as the region that is bounded by the graph of the function f(X)=x^3/6+2, the xaxis, x=-1, and x=1. QUESTION 9 · 1 POINT 23 Define R as the region that is bounded by the graph of the function f(2) +2, the x-axis, x = -1, and x = 1. Use 6 the disk method to find the volume of the solid of revolution when R is rotated around the z-axis. Submit an exact answer in terms 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...
1. y = -x/6 + 1, y = x/2 + 1, x = 6 Axis of revolution: y = 0. a) Sketch of the region bounded by the given functions and sketch the axis of revolution (1 point). b) Set up (but do not evaluate) an integral to determine the volume of the solid obtained by rotating the region bounded by the functions around the axis of revolution. Use the disk method or the cylindrical shells method (3 points). c)...
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...
You are given the table below. 16 20 4 8 12 X f(x) 12 2417 6 30 Use the table and n = 4 to estimate the following. Because the data is not monotone (only increasing or only decreasing), you should sketch a possible graph and draw the rectangles to ensure you are using the appropriate values for a lower estimate and an upper estimate. 20 f(x)dx lower estimate upper estimate Estimate the area of the region under the curve...
296 PRACTICE EXAM-AB-1 Consider the graphs of y=x/2 and y = cos(πx/3) shown in the figure above. The two graphs intersect at point P. Region R is bounded by the two graphs and the y-axis. Region Sis bounded by the two graphs and the x-axis. (a) Find the slope of the tangent line to y = cos(πx/3) at point P. (b) Find the area of R. (C) Find the area of S. (d) Set up, but do not evaluate, an expression for the volume of the solid...
Please help with 1-10 and please show all work thanks. Show all of your work neatly, and express solutions as exact answers unless otherwise requested. No credit will be given to solutions that have no work shown! BOX or CIRCLE your final answer. 1. Sketch a graph and shade the area of the region bounded by the following equations. Set up an integral that would give this area. 2x + y2 = 6 and y=x+1 2. Sketch a graph and...
3. Consider the region R, bounded by the function f(x) and the x and y values shown. Write down an integral for the volume of the solid obtained by revolving R about the given line. Indicate what method you use in each case. 3 f(x) 2 R (Disk, Washer, or Shell) 1 You do not need to simplify but be sure to include the proper bounds on your integrals. a) The y-axis. Method: b) The line y =1. Method: c)...
2/6 2" (10%) (a) Sketch the graphs of the two functions y=z(4-z) and y=z and mark the finite region (R) enclosed between them. (Identify (R) carefully!) (b) Let W be the volume of the solid of revolution obtained by revolving the above region (R) around the y-axis. (i) Use the shell method to write down the integral for W. (No need to evaluate the integral.) (ii) Repeat part(i) by using the disk method. 2/6 2" (10%) (a) Sketch the graphs...
1. Use the method of cylindrical shells to find the volume of the following solids rotation (i) Spin the region bound by y -Vx,y 0, x-1 around the y-axis; (ii) Twist the area bound by x -1+(y-2)2 andx- 2 about the x-axis; (iii) Rotate the region between y - x2 and y -6x-2x2 around the y-axis; (iv) Twirl the space between y V and x 2y about the line x 5 2. Use both methods discussed in class to compute...