Asked by Leslly
Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=6x about the line x=0using the method of disks or washers.
Answers
Answered by
Steve
the curves intersect at (0,0) and (6,36)
using washers of thickness dx, we have
v = ∫[0,6] π(R^2-r^2) dx
where R=6x and r=x^2
v = ∫[0,6] π(36x^2-x^4) dx = 5184π/5
To check, try using shells of thickness dy:
v = ∫[0,36] 2πrh dy
where r=y and h=√y-y/6
v = ∫[0,36] 2πy(√y-y/6) dy = 5184π/5
using washers of thickness dx, we have
v = ∫[0,6] π(R^2-r^2) dx
where R=6x and r=x^2
v = ∫[0,6] π(36x^2-x^4) dx = 5184π/5
To check, try using shells of thickness dy:
v = ∫[0,36] 2πrh dy
where r=y and h=√y-y/6
v = ∫[0,36] 2πy(√y-y/6) dy = 5184π/5
Answered by
Anonymous
How did u get all of that
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.