Asked by Em
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = (64 − x^2)^(1/4), y = 0, x = 6, x = 7; about the x-axis
y = (64 − x^2)^(1/4), y = 0, x = 6, x = 7; about the x-axis
Answers
Answered by
Steve
v = ∫[6,7] πr^2 dx
where r = y = ∜(64-x^2)
v = π∫[6,7] √(64-x^2) dx
= π(1/2 √(64-x^2) + 32 arcsin(x/8)) [6,7]
= π(√15/2 - √7 + 32(arcsin(7/8)-arcsin(3/4)))
where r = y = ∜(64-x^2)
v = π∫[6,7] √(64-x^2) dx
= π(1/2 √(64-x^2) + 32 arcsin(x/8)) [6,7]
= π(√15/2 - √7 + 32(arcsin(7/8)-arcsin(3/4)))
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.