Question

Calculate the volume of a rotating object if the area bounded by y = x ^ 2 and y = 6x-x ^ 2 is rotated around the line x = 3. Complete your answer with a sketch of the rotated area and the axis of rotation.

Answer #1

a)
Given the region bounded by y=1/x, x=7, y=7 and rotating around
x=7, find the volume.
b) Find the volume of the solid given by y=2x-x^2, while
rotating around the y-axis.

What is the volume of the solid obtained by rotating the region
bounded by the
curves y = −x^2 + 4x − 3 and y = 0 rotated about the y-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...

#6) a) Set up an integral for the volume of the solid S
generated by rotating the region R bounded by x= 4y and y= x^1/3
about the line y= 2. Include a sketch of the region R. (Do
not evaluate the integral).
b) Find the volume of the solid generated when the plane region
R, bounded by y^2= x and x= 2y, is rotated about the
x-axis. Sketch the region and a typical shell.
c) Find the length of...

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

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

Calculate the volume of the solid generated by rotating the
region bounded by the curves
x = 2y^2 and x = y^2 + 1 about the line y = -2

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...

Consider the region bounded by y=sqrt(x) and y=x^3
a) Find the area of this region
b) Find the volume of the solid generated by rotating this
region about the x-axis using washer
c) Find the volume of the solid generated by rotating this
region about the horizontal line y=3 using shells

Question3: ( You just need to provide the final answer)
a）Calculate the area of the region enclosed by y = cos(x) and y
= sin(x) between x = 0 and x = π/4 .
b) Find the volume of the solid obtained when the the region
bounded by y = √x and y = x^3 is rotated around the x-axis.
c) Find the volume of the solid obtained when the the region
bounded by y = x^2 and y =...

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