volume of rotation: y=x2−24y=x2−24 and y=6x−24y=6x−24 about the axis x=−3x=−3

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Khalifah

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volume of rotation: y=x2−24y=x2−24 and y=6x−24y=6x−24 about the axis x=−3x=−3

Use any method to find the volume of the solid obtained by rotating the region enclosed by the curves [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y=x2−24[/FONT] and [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y=6x−24[/FONT] about the axis [FONT=MathJax_Math-italic]x[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT]x=−3[/FONT].
 
Khalifah said:
Use any method to find the volume of the solid obtained by rotating the region enclosed by the curves [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y=x2−24[/FONT] and [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y=6x−24[/FONT] about the axis[FONT=MathJax_Math-italic]x[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT]x=−3[/FONT].
Click to expand...

These equations do not make sense!

Please check your post for accuracy and repost showing your work.
 
Khalifah said:
Use any method to find the volume of the solid obtained by rotating the region enclosed by the curves [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y=x2−24[/FONT] and [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y=6x−24[/FONT] about the axis [FONT=MathJax_Math-italic]x[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT]x=−3[/FONT].
Click to expand...
When you did your copy-n-paste from your online assessment in the posting box, you double-copied the equations. Were you unable to see this, when you'd posted?

My guess as to the intended exercise is as follows:


Use any method to find the volume of the solid obtained by rotating the region enclosed by the following curves:

. . . . .\(\displaystyle y\, =\, x^2\, -\, 24\)

. . . . .\(\displaystyle y\, =\, 6x\, -\, 24\)

...about the axis \(\displaystyle x\, =\, -3.\)


Is the above correct? Please provide confirmation or corrections.

When you reply, please include a clear listing of your efforts so far, starting with the algebra of finding the endpoints of the integration region, so we can see where you're getting stuck. Thank you! ;)
 
:idea: You can use the Preview Post button, before submitting posts, to see how your post will appear AND to proofread your typing.
 
Khalifah said:
Use any method to find the volume of the solid obtained by rotating the region enclosed by the curves [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y=x2−24[/FONT] and [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y=6x−24[/FONT] about the axis [FONT=MathJax_Math-italic]x[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT]x=−3[/FONT].
Click to expand...
Use any method to find the volume of the solid obtained by rotating the region enclosed by the following curves:

. . . . .[FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]y

. . . . .[FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]24[/FONT]

...about the axis [FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT]
Click to expand...

Did you try to draw the boundaries and figure out limits of integration?
 
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