Question

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

Answer #1

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

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

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...

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.

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 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=?

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.

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

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

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