Question

Consider the region S enclosed by the graphs of y=x^3-6^2+9x and y=x/2 . Determine which solid has the greater volume, and by how much: (a) The solid generated by revolving S about the x-axis; (b) The solid generated by revolving S about the line y=4.

Answer #1

there are 5 parts to this question
1.Find the area of the region R enclosed by the graphs of y = x
2 , the y-axis and the line y = 4
2.Find the volume of the solid generated by revolving the region
in problem 1 about the x-axis.
3.Use the cylindrical shell method to find the volume of the
solid generated by revolving the region in problem 1 about the
y-axis.
4.Find the volume of the solid generated by...

Find the volume of the solid generated by revolving the region
bounded by the graphs of y = e x/4 , y = 0, x = 0, and x = 6 about
the x−axis.
Find the volume of the solid generated by revolving the region
bounded by the graphs of y = √ 2x − 5, y = 0, and x = 4 about the
y−axis.

Consider the solid S described below. The base of S is the
region enclosed by the parabola y = 1 - 9x^2 and the x-axis.
Cross-sections perpendicular to the x-axis are isosceles triangles
with height equal to the base. Find the volume V of this solid.

1) Find the volume of the solid obtained by rotating the region
enclosed by the graphs about the given axis. ?=2?^(1/2), y=x about
y=6 (Use symbolic notation and fractions where needed.)
2) Find the volume of a solid obtained by rotating the region
enclosed by the graphs of ?=?^(−?), y=1−e^(−x), and x=0 about
y=4.5.
(Use symbolic notation and fractions where needed.)

Find the volume of the solid generated by revolving the region
bounded by y = sqrt(x) and the lines and about y=2 and x=0
about:
1) the x-axis.
2) the y-axis.
3) the line y=2.
4) the line x=4.

Find the volume of the solid generated by revolving the region
bounded by the graphs of the equations about the
x-axis.
y = 1 / sqrt of (7x+3)
x = 0
y = 0
x = 7

1. Use the washer/disc method to determine the volume of the
solid.
a) Region enclosed by y = x^3 - 4x, the x-axis, x = 1, and x = 3
rotated about the x-axis.
b) Region enclosed by y=1/x and y 5/2 - x rotated about the line
x = 3.

Find the volume of the solid generated by revolving the region
enclosed by the triangle with vertices(3,1),(3,5), and(6,5) about
the y-axis.

3.
(a) Find the volume of the solid generated by revolving the
region bounded by the graphs of the given equations around the
x-axis.
? = 0, ? = ? 3 + ?, ? = 1
(b) Find the volume of the solid generated by revolving the
region from part (a) around the y-axis

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

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