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.
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
Find the volume of the solid obtained by rotating the region
bounded by y = x 3 , y = 1, x = 2 about the line y = −3.
Sketch the region, the solid, and a typical disk or washer
(cross section in xy-plane).
Show all the work and explain thoroughly.
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
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.
⃗ 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