  # Use the method of cylindrical shells to find the volume of thesolid, generated by the enclosed region when rotating throughone revolution.y=6x-2x, y=x, Rotation about x-0Answer the following:1111Sketch the graphs and show all information to determine thevolume using the method specified above.aSet-up the formulation for the volume of the approximatingrectangle (i.e. elemental volume).bSpecify the domain of the enclosed region..cSet-up the integral and if possible, simplify it.d

Question

Hi, could you let me know if the integral for part (c) of the attached image is V=integral from 0 to 3 of 2pi x((6x-2x^2)-x^2))dx ? Thank you. help_outlineImage TranscriptioncloseUse the method of cylindrical shells to find the volume of the solid, generated by the enclosed region when rotating through one revolution. y=6x-2x, y=x, Rotation about x-0 Answer the following: 11 11 Sketch the graphs and show all information to determine the volume using the method specified above. a Set-up the formulation for the volume of the approximating rectangle (i.e. elemental volume). b Specify the domain of the enclosed region. .c Set-up the integral and if possible, simplify it. d fullscreen
check_circleExpert Solution
Step 1

Consider the enclosed region by  equation 1 and equation 2

Step 2

In the graph blue represent to equation 2 and red represent to equation 1

Step 3

Now solve the both equation for the inte... help_outlineImage Transcriptionclose6x-2x22 =X 6х — х? + 2х? 3x? — 6х %— 0 3x (х- 2) -0 Then, solutins are x=0, x-2 fullscreen

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### Integration 