Question

a.) Let S be the solid obtained by rotating the region bounded by the curves y=x(x−1)^2 and y=0 about the y-axis. If you sketch the given region, you'll see that it can be awkward to find the volume V of S by slicing (the disk/washer method). Use cylindrical shells to find V

b.) Consider the curve defined by the equation xy=12. Set up an integral to find the length of curve from x=a to x=b. Enter the integrand below

Answer #1

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et S be the solid obtained by rotating the region bounded by the
curves ?=sin(?2) and ?=0 with 0≤?≤root(?) about the ?y-axis. Use
cylindrical shells to find the volume of S.
Volume =

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...

Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line, using the
disk/washer method. Sketch the region, the solid, and a typical
disk or washer.

Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
y = 2 + sec(x),
−π
3
≤ x ≤
π
3
, y = 4; about
y = 2
V =
Sketch the region.
Sketch the solid, and a typical disk or washer.

Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
y = 5x4, y = 5x, x ≥
0; about the x-axis
Find the area of the region enclosed by the given curves.
y = 3 cos(πx), y = 12x2 −
3
Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
2x = y2, x = 0, y =
5; about the...

3. Find the volume of the solid of revolution. The region is
bounded by y= 4x and y = x^3 and x ≥ 0.
a) Make a sketch.
b) About the x axis (disk/washer method).
c) About the x axis (cylindrical shells).
d) About the y axis (disk/washer method).
e) About the y axis (cylindrical shells).

Consider the solid obtained by rotating the region bounded by
the given curves about the x-axis. y = 5 x^3 y = 5 x x >= 0 Find
the volume V of this solid. V =

Find the volume V of the solid obtained by rotating the region
bounded by the given curves about the specified line. 2x = y^2, x =
0, y = 5; about the y-axis
sketch the region, sketch the solid

Use cylindrical shells to find the volume of the solid obtained
by rotating the region bounded on the right by the graph of
g(y)=9√y and on the left by the y-axis for 0≤y≤8, about the x-axis.
Round your answer to the nearest hundredth position.
V=?

Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis. Your set-up
must include a graph of the region and an example of the rectangle
used or one disk/washer or shell (depending on the method
used).
1. y = x3 , y = 0, x =1 about the x-axis
2. y = SQRT(x −1), x = 5, y = 0 about the y-axis
3. y = 4/x, x =1, x...

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