anonymous
  • anonymous
find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y =(x^2)+1 , y = 9 - (x^2) about y = -1
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
freckles
  • freckles
I like a little visual. |dw:1443749174250:dw|
freckles
  • freckles
find the x-coordinates of the intersections there for the limit part
anonymous
  • anonymous
\[\pi[\int\limits_{-2}^{2}(10-x^2)^2-\int\limits_{-2}^{2}(x^2+2)^2\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
this is what i have so far
anonymous
  • anonymous
i think its wrong because i keep getting the wrong answer
freckles
  • freckles
|dw:1443749494904:dw| your radi look right
freckles
  • freckles
let me check your x-coordinates of your interesections
freckles
  • freckles
\[x^2+1=9-x^2 \\ 2x^2=8 \\ x^2=4 \\ x= \pm 2\]
freckles
  • freckles
what did you get as the answer after integration ?
anonymous
  • anonymous
the final answer or do you want me to integrate it?
anonymous
  • anonymous
ill integrate
freckles
  • freckles
give the answer and I will check it then if the answer is not what I have I might ask you to show me the integration
anonymous
  • anonymous
i got 864pi for the final answer but wolframalpha says 256pi
freckles
  • freckles
ha so it is the integration
freckles
  • freckles
\[(10-x^2)^2=100-20x^2+x^4 \\ (2+x^2)^2=4+4x^2+x^4\] you get this for the expansion part?
freckles
  • freckles
the difference would be ... \[96-24x^2 \] \[\pi \int\limits_{-2}^{2} (96-24x^2) dx \\ \pi( 96x-8x^3)|_{-2}^{2}\]
anonymous
  • anonymous
\[i get 100x-\frac{ 20x^3 }{ 3 }+\frac{ x^5 }{ 5 }-\frac{ x^5 }{ 5 }-\frac{ 4x^3 }{ 3 }+4x\]
freckles
  • freckles
I think that one term should be -4x
freckles
  • freckles
not +4x
anonymous
  • anonymous
oh yes i see that
freckles
  • freckles
but anyways you should be able to combine like terms after making that correct and get what I have above
freckles
  • freckles
it is fine what you did integrate then simplify I prefer to simplify then integrate most of the time
anonymous
  • anonymous
\[[100(2)-\frac{ 20(2)^3 }{ 3 }-\frac{ 4(2)^3 }{ 3 }-4(2)]-[100(-2)-\frac{ 20(-2)^3 }{ 3 }-\frac{ 4(-2) }{ 3 }-4(-2)]\]
freckles
  • freckles
ick why not clean up before pluggin in numbers
freckles
  • freckles
if you prefer this, this is fine... but it looks gross to me :p
anonymous
  • anonymous
youre right but ive been working on this problem all day so im tryin to be explicit
anonymous
  • anonymous
ok i got it thank you
freckles
  • freckles
\[[200-\frac{160}{3}-\frac{32}{3}-8]-[-200+\frac{160}{3}+\frac{32}{3}+8] \\ (200+200)+(-\frac{160}{3}-\frac{160}{3})+(\frac{-32}{3}-\frac{32}{3})+(-8-8) \\ (400)+(\frac{-320}{3})+(\frac{-64}{3})+(-16) \\ \\ (400-16)+(\frac{-320}{3}+\frac{-64}{3}) \\ (384)+(\frac{-384}{3}) \\ 384(1-\frac{1}{3}) \\ 384(\frac{2}{3}) \\ \frac{384}{3}(2) \\ (128)(2) \\ 256\]
anonymous
  • anonymous
my math was just a little off
freckles
  • freckles
is the way I would have continued from your last step there
freckles
  • freckles
and of course shove the pi in
anonymous
  • anonymous
i got all the integration and the equation and messed up on the algebra
freckles
  • freckles
I think if you have simplified before integration would have made it tons easier
anonymous
  • anonymous
il keep that in mind these problems are taking longer and longer
freckles
  • freckles
\[\int\limits _{-2}^{2}[(10-x^2)^2-(x^2+2)^2 ]dx\\ \int\limits_{-2}^2 [(100-20x^2+x^4)-(x^4+4x^2+4)] dx \\ \int\limits_{-2}^2 [(100-4)+(-20x^2-4x^2)+(x^4-x^4)] dx \\ \int\limits_{-2}^2 [96-24x^2] dx \\ 96x-24 \frac{x^3}{3} |_{-2}^2 \\ 96x-8x^3|_{-2}^2 \\ (96 \cdot 2 -8(2)^3)-(96 \cdot (-2)-8(-2)^3) \\ (192-64)-(-192+64) \\(192+192)+(-64-64) \\ 384+(-128) \\ 256\]
freckles
  • freckles
just in case you wanted to see how I would tackled the integration and the after part

Looking for something else?

Not the answer you are looking for? Search for more explanations.