Question

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the give line. (a) Graph the region (b) Graph the solid (c) Sketch a typical shell. (d) Determine the variable of integratoin (e) Draw and label the radius and height of the shell. Describe their length. (f) Find the volume.

y = 4x, y = 0, x = 2; revolve about the line x = -3

Answer #1

we are given equations as

revolve about the line

**(a) , (b), (c)**

**Graph :**

we can draw graph

**(d)**

Since,

It revolves about the line x = -3

and we can use shell method

so, variable of integration =x

**(e)**

**(f)**

Bound is from 0 to 2

we can use formula

now, we can solve each integrals

and then combine them

**...........Answer**

Use shell method to find the volume of the solid generated by
revolving the region bounded by y=4−x, y=2 ,x=0 about x-axis.
Sketch the region.

Use the shell method to find the volume of the solid generated
by revolving the region bounded by the given curves and lines about
the y-axis.
y = x 2 - 4, y = 3x, x = 0, for x ≥ 0

Use the shell method to find the volume of the solid generated
by revolving the region bounded by y=3x-2, y=sqrt.x, and x=0 about
the y-axis.
The volume is in cubic units.

Use the shell method to find the volume of the solid generated
by revolving the plane region about the line x = 4.
y = x2
y = 4x − x2

Use the shell method to find the volume of the solid
generated by revolving the regions bounded by the given curves
about the given lines.
a. The y-axis
b. The line x=4
c. The line x= (-1)
d. The x-axis
e. The line y=7
f. The line y=(-2)
For: y=3x, y=0, x=2

Set up an integral using the shell method to find the volume of
the solid generated by revolving the area bounded by the graphs of
the equations y=1/(x+2) y =0, x = 0 and x=5 about the line x=
-3.Sketch a graph of the region, highlighting your slice

(a) Find the volume of the solid generated by revolving the
region bounded by the curves y=x2 andy=4x−x2 abouttheliney=6.
[20marks]
(b) Sketch the graph of a continuous function f(x) satisfying
the following properties: (i) the graph of f goes through the
origin
(ii) f′(−2) = 0 and f′(3) = 0.
(iii) f′(x) > 0 on the intervals (−∞,−2) and (−2,3).
(iv) f′(x) < 0 on the interval (3,∞).
Label all important points. [30 marks]

Find the volume of the solid generated by revolving the plane
region bounded by the graphs of y= \sqrt{x} , y=0, x=5, about the
line x=8.
Find the volume using: a) DISK/WASHER Method b) SHELL METHOD

Find the volume of the solid generated by revolving the plane
region bounded by the graphs of y= \sqrt{x} , y=0, x=5, about the
line x=8.
Find the volume using: a) DISK/WASHER Method b) SHELL METHOD

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.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 15 minutes ago

asked 22 minutes ago

asked 30 minutes ago

asked 36 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago