Find the volume of the solid generated by revolving the region
bounded by y = sqrt(x) and the lines and y=2 and x=0 about:
1) the x-axis.
2) the y-axis.
3) the line y=2.
4) the line x=4.
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 solid of revolution obtained
by revolving the planeregion bounded by ? = ? − ?²
, ? = 0 about line ? = 2 .
Mathematics Civil Engineering Please solve this
question in 15 minutes is necessary
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 by
the curves about the given axis.
y = cos(πx/2), y = 0, 0 ≤ x ≤ 1; about the y-axis.
Find the volume of the solid obtained by revolving the region
bounded above by the curve y = f(x) and below by the curve y= g(x)
from x = a to x = b about the x-axis.
f(x) = 3 − x2 and g(x) = 2; a =
−1, b = 1
Consider the region bounded by y = x2 −6x+9 and y = 9−3x. Set up, but do not evaluate, an integral to find the volume of the solid generated by revolving this region about the x-axis.
set
up an integral to find the volume of the solid generated when the
region bounded by
y=x^2 and y=3x
i) rotate about x-axis using washer method
ii) Rotate about y-axis using washer method
iii) rotate abt y= -2 using the shell method
iv) rotatate about x=10 using the shell method
Set up an integral to find the volume of the solid generated
when the region bounded by y = x^3 and y = x^2 is (a) Rotated about
the x-axis using washers (b) Rotated about the y-axis using shells
(c) Rotated about the line y = −2 using either washers or
shells.