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 = 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 the circle x2 +
(y−2)2 = 1 about the x-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.

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 cylindrical shells, find the volume of the solid obtained
by taking the region between y=x and y=x^2 for 1≤x≤3 and rotating
it about the the line x=−4.

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...

find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line. y=sqrt x-4 ,
y=0 and x=9 rotated about the x axis

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...

Use the method of cylindrical chills to find the volume
generated by rotating the region bounded by the given curves about
the y-axis. y=x^3, y=0, x=1, x=2

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