a,d,e,f. please!! 28 The following problems are to be done with triple integrals. You may usecylindrical or spherical coordinates if you wish.Find the volume of the solid bounded above by the graph of x² + y? +z? = 5 andbelow by the graph of x2 + y? = 4z.b Find the volume of the solid bounded by the graphs of x² + y² + z² = a²,+y?% (tan²a)2, with z 2 0, and x? + y? =(tan?pz?, with z 2 0.Here a >0 and 0

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1)Sketch the solid obtained by rotating the region bound byy=2√x and y=x, about the line x =−2. 2)Write the expression for the area of a representative washer 3)Set up and solve the definite integral used to calculate the volume of the solid in (1)
SET UP the integral necessary to find the volume ofthe solid for the shaded area revolved about the givenaxis using ONLY the shell method. Equations: x=(1/2)y-1 and y=x2-2x+2 Revolved around the x-axis, with an integral with respect to x.
Consider the region bounded to the right by the graph of x=sin(5y)+10y, to the left by the y-axis, and above and below by y=2π3 and y=π3. Using the shell method, what is the volume of the solid of revolution obtained by rotating this region about the x-axis? Enter an exact value in terms of π.
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A solid is formed by rotating the region bounded by the curve y=e^(−3x/2) and the x-axis between x=0 and x=1, around the x-axis. The volume of this solid is (π/3)⋅(1−e^(−3)). Assuming the solid has constant density δ, find x¯ and y¯
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#2. Consider the region R between y = sin x and the x-axis for 0 ≤x ≤π.(a) Find the volume of the solid obtained by rotating R about the y-axis.(b) Find the volume of the solid obtained by rotating R about the x-axis.
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Find the volume of the solid bounded above by the graph of x2 + y2 +z2 = 5 and below by the graph of x2 +y? = 4z.