SHELL METHOD HELP

[jake.bradley]

Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions y=x^2, y=8-x^2 and x=1 about the y-axis.

AND

Shell Method to computer volume obtained by rotating the region enclosed by functions y=x^4 and y=x^(1/4) about the y-axis.

No idea where to start, please please help.

 

[Deleted member 4993]

Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions y=x^2, y=8-x^2 and x=1 about the y-axis.

AND

Shell Method to computer volume obtained by rotating the region enclosed by functions y=x^4 and y=x^(1/4) about the y-axis.

No idea where to start, please please help.

First sketch the functions - find the points of intersections - define the limits.

Look at the method shown in:

viewtopic.php?f=3&t=39664

Please show us your work, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[jake.bradley]

I don't know where to being. I don't get where they got the limits from or anything. I know the formula for Shell Method but nothing else.

 

[Deleted member 4993]

I don't know where to being. I don't get where they got the limits from or anything. I know the formula for Shell Method but nothing else.

You are not listening ...

First sketch the functions - on graph paper or using graphing calculator.

Then find the points of intersection - those will tell you about the limits.

 

[jake.bradley]

intersects at x = -2 and x = 2

so from -2 to 2?

 

[BigGlenntheHeavy]

\(\displaystyle 1st \ one: \ 2\pi\int_{1}^{2}x(8-2x^2)dx \ = \ 9\pi, \ now \ can \ you \ figure \ it \ out?\)

 

[BigGlenntheHeavy]

\(\displaystyle 2nd \ one:\)

\(\displaystyle Shell:\)

\(\displaystyle 2\pi\int_{0}^{1}x (x^{1/4}-x^4)dx \ = \ \frac{5\pi}{9}\)

\(\displaystyle Disc:\)

\(\displaystyle \pi\int_{0}^{1}(y^{1/2}-y^8)dy \ = \ \frac{5\pi}{9}\)

\(\displaystyle Note: \ my \ mistake, \ as \ the \ above \ is \ revolved \ around \ the \ x \ axis \ instead \ of \ y \ axis, \ but \ one\)

\(\displaystyle gets \ the \ same \ results.\)

\(\displaystyle See \ graph:\)

[attachment=0:20cqek03]jkl.jpg[/attachment:20cqek03]

 

[BigGlenntheHeavy]

\(\displaystyle Another \ thing \ Jake, \ no \ need \ to \ become \ obstreperous \ just \ because \ (my \ self \ included) \ some\)

\(\displaystyle moderator \ was \ a \ little \ precipitant \ in \ responding \ to \ one \ of \ your \ queries, \ as \ such \ is \ life\)

\(\displaystyle and \ we \ must \ get \ on \ with \ it. \ In \ closing, \ all \ I \ can \ say \ to \ you \ is \ that \ life \ isn't \ always \ fair,\)

\(\displaystyle but \ then \ I \ ask \ you \ - \ where \ is \ it \ etched \ in \ stone \ that \ life \ is?\)