Question
In: Math
Use the method of cylindrical shells to find the volume V generated by rotating the region...
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
Solutions
Expert Solution
Given curve is:
, 
and 
.
the given curve is rotated about x-axis.
finding intersection points:
put x-0,
hence, intersection point is (0,1)
considered a small cylindrical shell of radius 
and height 
integrate it over the y-axis.
The corresponding volume of the curve is defined as:
milcah answered 2 years agoRelated Solutions
Use the method of cylindrical shells to find the volume generated by rotating the region bounded...
Use the method of cylindrical shells to find the volume
generated by rotating the region bounded by the given curve about
the specified axis.
1.y=sqrt(x-1) y=0 x=5;
about the line y=3
2. y=5, y=x+4/x ;
about the line x=-1
Use the method of cylindrical shells to find the volume generated by rotating the region bounded...
Use the method of cylindrical shells to find the volume
generated by rotating the region bounded by
the curves about the given axis.
y = cos(πx/2), y = 0, 0 ≤ x ≤ 1; about the y-axis.
Use cylindrical shells to find the volume of the solid generated by rotating the given region...
Use cylindrical shells to find the volume of the solid generated
by rotating the given region about the x-axis.
y=e^x, y=1, x=2
1) Use cylindrical shells to find the volume of the solid obtained by rotating the region...
1) Use cylindrical shells to find the volume of the solid
obtained by rotating the region bounded by y=x^2, y=0, and x=5,
about the y-axis.
V=
2) Use cylindrical shells to find the volume of the solid
obtained by rotating the region bounded by y=x^2, y=0, and x=6,
about the yy-axis.
V=
3)The region bounded by f(x)=−3x^2+15x+18f(x)=-3x2+15x+18,
x=0x=0, and y=0y=0 is rotated about the y-axis. Find the
volume of the solid of revolution.
Find the exact value; write answer without...
Use the shell method to find the volume of the solid generated by revolving the region...
Use the shell method to find the volume of the solid generated
by revolving the region bounded by the line y equals 2x plus 3 and
the parabola y equals x squared about the following lines. a. The
line x equals 3 b. The line x equals minus 1 c. The x-axis d. The
line y equals 9
Find the volume of the figure created by rotating the region enclosed by the graphs of...
Find the volume of the figure created by rotating the region
enclosed by the graphs of y = x^2 and y = x^3
a) around the x-axis
b) around the y-axis
a. Find the volume of the solid obtained by rotating the region enclosed by the curves...
a. Find the volume of the solid obtained by rotating the region
enclosed by the curves y = 4 x^2 , y = 5 − x^2 about the line y =
11
b. Find the volume of the solid obtained by rotating the region
enclosed by the graphs about the given axis.
y = 2sqt (x), y=x, about x=-20.
Please leave your answer in fraction if
possble
Find the volume of the solid obtained by rotating the region enclosed by the graphs of...
Find the volume of the solid obtained by rotating the region
enclosed by the graphs of y=9−x, y=3x−3 and x=0 about the
y-axis.
Find the volume of the solid of revolution that is formed by rotating the region bounded...
Find the volume of the solid of revolution that is formed by
rotating the region bounded by the graphs of the equations given
around the indicated line or axis
1.- y=9-x^2, y=0, around the x axis
2.- y=√x-1, x=5, y=0, around the x=5
3.- y=1-x, x=0, y=0, around the y= -2
4.- y=x^2, x=0, y=3, around the y axis
Use the Disk/Washer Method to find the volume of the solid of revolution formed by rotating...
Use the Disk/Washer Method to find the volume of the solid of
revolution formed by rotating the region about each of the given
axes.
14. Region bounded by: y=4 - x^2 and y=0.
(a) the x-axis (c) y= -1
(b)y=4 (d) x=2
AND
17. Region bounded by: y=1/ sqrt((x^2) +1), x= -1, x=1 and the
x-axis.
Rotate about:
(a) the x-axis (c) y= -1
(b) y=1
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