Question

Consider the region R bounded by y = sinx, y = −sinx , from x = 0, to x=π/2.

(1) Set up the integral for the volume of the solid obtained by
revolving the region R around

x = −π/2

(a) Using the disk/washer method.

(b) Using the shell method.

(2) Find the volume by evaluating one of these integrals.

Answer #1

Let R be the region bounded by y = ln(x), the x-axis, and the
line x = π.
a.Usethecylindrical shell method to write a deﬁnite integral
(BUTDONOTEVALUATEIT) that gives the volume of the solid obtained by
rotating R around y-axis
b. Use the disk (washer) method to write a deﬁnite integral (BUT
DO NOT EVALUATE IT) that gives the volume of the solid obtained by
rotating R around x-axis.

Let R be the region of the plane bounded by y=lnx and the x-axis
from x=1 to x= e. Draw picture for each
a) Set up, but do not evaluate or simplify, the definite
integral(s) that computes the volume of the solid obtained by
rotating the region R about they-axis using the disk/washer
method.
b) Set up, but do not evaluate or simplify, the definite
integral(s) that computes the volume of the solid obtained by
rotating the region R about...

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...

The region is bounded by y=2−x^2 and y=x. (a) Sketch the region.
(b) Find the area of the region. (c) Use the method of cylindrical
shells to set up, but do not evaluate, an integral for the volume
of the solid obtained by rotating the region about the line x = −3.
(d) Use the disk or washer method to set up, but do not evaluate,
an integral for the volume of the solid obtained by rotating the
region about...

Let B be the region bounded by the part of the curve y = sin x,
0 ≤ x ≤ π, and the x-axis. Express (do not evaluate) the volume of
the solid obtained by rotating the region B about the y-axis as
definite integrals
a) using the cylindrical shell method
b) using the disk method

R is the region bounded by ? = √? − 1, ? = 2, and the
x-axis.
a) Set up the integral you would use to find the volume of the
solid formed by revolving R around the y-axis.
b) Set up the integral you would use to find the volume of the
solid formed by revolving R around the line ? = −3
c) Set up the integral you would use to find the volume of the
solid formed...

Consider the region bounded by ? = 4? , ? = 1 and x-axis. Set
up the appropriate integrals
for finding the volumes of revolution using the specified
method and rotating about the specified axis. Be sure to first
sketch the region and draw a typical cross section. SET UP THE
INTEGRALS ONLY. DO NOT evaluate the integral.
a) Disc/washer method about the x-axis
b) Shell method about the y-axis
c) Disc/washer method about the line ? = 2.
d)...

Let R be the region bounded by y = x2 + 1, y = 0, x =
1, and x = 2. Graph the region R. Find the
volume of the solid generated when R is revolved
about the y-axis using (a) the Washer Method and
(b) the Shell Method.

Find the volume of the solid generated by revolving the plane
region bounded by the graphs of y= \sqrt{x} , y=0, x=5, about the
line x=8.
Find the volume using: a) DISK/WASHER Method b) SHELL METHOD

Find the volume of the solid generated by revolving the plane
region bounded by the graphs of y= \sqrt{x} , y=0, x=5, about the
line x=8.
Find the volume using: a) DISK/WASHER Method b) SHELL METHOD

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