Asked by bob
Consider the solid obtained by rotating the region bounded by the given curves about the x-axis.
y = 6 x^6 , y = 6 x , x >= 0
Find the volume V of this solid.
y = 6 x^6 , y = 6 x , x >= 0
Find the volume V of this solid.
Answers
Answered by
drwls
The curves intersect at x = 0 and x = 1. The region bounded between those curves has y-separation of 6(x-x^6).
For the total enclosed area, integrate that function times dx from x=0 to x=1.
For the total enclosed area, integrate that function times dx from x=0 to x=1.
Answered by
drwls
I forgot that you wanted the volume of the solid obtained by rotating the curves about the x axis. This changes the formula to
Integral of 36 pi (x^2 - x^12) dx
...0 to 1
Integral of 36 pi (x^2 - x^12) dx
...0 to 1
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.