Asked by Corey
Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by
y = x^3
y = 16 x
about the x-axis.
y = x^3
y = 16 x
about the x-axis.
Answers
Answered by
Corey
Solved
Answered by
Steve
The curves intersect at (0,0) and (4,64)
Using discs of thickness dx, we have
v = ∫[0,4] π(R^2-r^2) dx
where R=16x and r=x^3
v = ∫[0,4] π((16x)^2-(x^3)^2) dx = 65536π/21
or, you can use nested shells of thickness dy, where the height of the shells is the distance between the curves.
v = ∫[0,64] 2πrh dy
where r=y and h = ∛y - y/16
v = ∫[0,64] 2πy(∛y - y/16) dy = 65536π/21
Using discs of thickness dx, we have
v = ∫[0,4] π(R^2-r^2) dx
where R=16x and r=x^3
v = ∫[0,4] π((16x)^2-(x^3)^2) dx = 65536π/21
or, you can use nested shells of thickness dy, where the height of the shells is the distance between the curves.
v = ∫[0,64] 2πrh dy
where r=y and h = ∛y - y/16
v = ∫[0,64] 2πy(∛y - y/16) dy = 65536π/21
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.