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2. a) The area between the curve y= Vx,0 5x Sa and the x axis rotates...
1. The area between the part of the curve-6x 8 above the x-axis and the x-axis itself is 2. The area below y 4x -x and above y 3 (for1 xS 3) is revolved around the x-axis. 3. The areas between the following portions of curves and the x-axis are revolved around the revolved by an angle 2π around the x-axis. Find the volume swept out. Find the volume swept out. y-axis. Find the volume swept out. (a) y- betweenx...
1) 2) Find the surface area of the volume generated when the curve y = Vx revolves around the x-axis from (1, 1) to (16, 4). Interactive 3D Graph Help -20 -10 10 20 2-3 Calculate the arc length over the given interval. y : **?- in(x), (1,7) x
The region enclosed by y = Vx and y = 5x is rotated around the x-axis. Choose the integral that can be used to find the volume of the solid of revolution. & S (x - 12 ) dx = [" (432 – y") dy
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...
3. Sketch the graph of the curve y vx' -5x + 6 = x (x-2)(x-3).
only number 5-7. Just set up no solve. show all work 1) Rotate the area bound by f(x): 2x + 1, y : O, x-1, and x : 4 around the x- 2) Rotate the area bound by y : x2 , y :0, and x-2 around the y-axis. #3-7: Draw a graph and setup the integral, including boundaries for determin the solid created. You do NOT need to evaluate the integrals. 3) Rotate the area bound byy and ya...
1. Find the area between the graph x(t)=t^2, y(t)=t^2 + 2 and the x-axis when 0 is less than or equal to t and t is less than or equal to 4. 2. Find the surface area when the curve, x(t)=e^t + e^-t; y(t)=5 - 2t with 0 less than +t which is less than or equal to 3 and rotation about the x-axis. Please answer both problems if possible with work. Thank you in advance. 1. Find the area...
5. Find the area of the surface obtained by rotating the curve y=Vx on the interval [0,1] around the y-axis. 6. Evaluate the integral dx (x+1)
21. Find the area between the parabola y = x2 + 5x and the x-axis between x=0 and x=2 by calculating the limit of the Riemann sum lim. ] [)* + 5%) i=1
10. Neatly sketch the region enclosed by the graph of y = Vx, the x-axis, and x = 3. Find the volume of the solid generated by revolving this region around the axes given below. (Use the method of your choice.) Set up an INTEGRAL and then evaluate it using your calculator. a.) About the x-axis b.) About the y-axis c.) About the line x = 4