Question

Use the method of cylindrical shells to find the volume of the solid found by revolving the region bounded by y=2x and y=x^2 about the y-axis.

For full credit, I expect to see the following: A graph of the bounded region between the two functions. A representative cylinder. Algebraic solutions for points of intersection. You won’t get full credit if you only write the points of intersection without showing the algebra. The set up for the integral(s). Anti-derivative(s). Work and/or verbal explanation of how to plug in the points. The final answer. Box your final answer.

Answer #1

Use the method of cylindrical shells to find the volume of the
solid obtained by rotating the region bounded by x = − 3 y 2 + 12 y
− 9 , x = 0 about the x-axis.

Using the Shells method, find the volume of the solid generated
by revolving the region bounded by
y = 5 - x, y = 0, x = 0
about the line y = -1.

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

Use the method of cylindrical shells to ﬁnd the volume of the
solid obtained by rotating the region bounded by the circle x2 +
(y−2)2 = 1 about the x-axis.

Use the method of cylindrical shells to find the volume
generated by rotating the region bounded by the given curves about
the y-axis.
y=12x-3x2, y=3x

Use the method of cylindrical shells to find the volume
generated by rotating the region bounded by the given curves about
the y-axis.
y =
4x2, y
= 24x − 8x2

Use the method of cylindrical shells to find the volume
V generated by rotating the region bounded by the given
curves about the specified axis.
y = ex, x = 0, y = 7π; about
the x-axis

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=?

Use the method of cylindrical shells to find the volume
V generated by rotating the region bounded by the given
curves about the specified axis.
y = 11
sqrt(x), y =
0, x =
1; about x = −4

1. Use cylindrical shells to find the volume of the solid
generated when the region enclosed by the given curves is revolved
about the x-axis.
a.) x = 4y^2 - y^3 and x=0
b.) y= x^2 ,x = 1 and y= 0
2. Use cylindrical shells to find the volume of the solid
generated when the region enclosed by the given curves is revolved
about the y-axis.
c.) y =e^x , y=e^-x and x = 1
d.) y = x^3...

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