Question

Using any method, SET UP, but do NOT evaluate, an integral representing the volume of the solid obtained by rotating the region bounded by the curves y = 1/x , y = 0, x = 1, x = 3 about (a) the line y = −1 (b) the y-axis

Answer #1

Using any method, SET UP, but do NOT evaluate, an integral
representing the volume of the solid obtained by rotating the
region bounded by the curves y = 1 x , y = 0, x = 1, x = 3 about
(a) the line y = −1 (b) the y-axis.

1. Use the shell method to set up and evaluate the integral that
gives the volume of the solid generated by revolving the plane
region about the line x=4.
y=x^2 y=4x-x^2
2. Use the disk or shell method to set up and evaluate the
integral that gives the volume of the solid generated by revolving
the region bounded by the graphs of the equations about each given
line.
y=x^3 y=0 x=2
a) x-axis b) y-axis c) x=4

Set up, but do not evaluate, the integral for the volume of the
solid obtained by rotating the region enclosed by y=\sqrt{x}, y=0,
x+y=2 about the x-axis. Sketch
a) By Washers
b) Cylindrical shells

1) Set up, but do not evaluate, an integral to find the volume
when the region bounded by y=1, y=tanx and the y-axis is rotated
about the following lines:
a) The x-axis
b) The y-axis
c) The line y=2
d) The line x=3
e) The line x= -1
2) Set up, but do not evaluate, an integral to find each of the
following:
a) The volume that results when the region in the first quadrant
bounded by y=sinx, y=1 and...

Using the Method of Cylindrical Shells, find a definite integral
that gives the volume V of the solid S obtained by rotating the
region R bounded by curves: y=sqrt[x] ,and y=0 about the
x-axis.
There is a 3rd line at x=4

#6) a) Set up an integral for the volume of the solid S
generated by rotating the region R bounded by x= 4y and y= x^1/3
about the line y= 2. Include a sketch of the region R. (Do
not evaluate the integral).
b) Find the volume of the solid generated when the plane region
R, bounded by y^2= x and x= 2y, is rotated about the
x-axis. Sketch the region and a typical shell.
c) Find the length of...

Use a detailed analysis to set up but not evaluate an integral
for the volume Z of the solid generated by revolving the region
bounded by the curves 2x = y^2, x = 0, and y = 4 about the
y-axis.

Set up an integral to find the volume of solid obtained by
rotating about the given axis, the region bounded by the curves
y=2x and x= sqrt 2y. Sketchh!! Axis - Y axis (Washer and Shell)

Set up the integral. you do NOT have to
integrate.
A region is bounded by the x-axis and y = sinx with 0 ≤
x ≤ π. A solid of revolution is obtained by rotating that region
about the line y =−2.

Consider the region in the xy-plane bounded by the curves y =
3√x, x = 4 and y = 0.
(a) Draw this region in the plane.
(b) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the x-axis using the cross-section method.
(c) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the y-axis using the shell method.
(d) Set up the integral...

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