Asked by alex
Find the exact area of the surface obtained by rotating the given curve about the x-axis.
x=t^3, y=t^2, 0 ≤ t ≤ 1
x=t^3, y=t^2, 0 ≤ t ≤ 1
Answers
Answered by
Steve
?[0,1] 2?x ds
= ?[0,1] 2?x?(x'^2 + y'^2) dt
= ?[0,1] 2?t^3?((3t^2)^2 + (2t)^2) dt
Not an easy one -- it will involve integration by parts.
http://www.wolframalpha.com/input/?i=%E2%88%AB%5B0,1%5D+(2%CF%80t%5E3%E2%88%9A((3t%5E2)%5E2+%2B+(2t)%5E2))+dt
= ?[0,1] 2?x?(x'^2 + y'^2) dt
= ?[0,1] 2?t^3?((3t^2)^2 + (2t)^2) dt
Not an easy one -- it will involve integration by parts.
http://www.wolframalpha.com/input/?i=%E2%88%AB%5B0,1%5D+(2%CF%80t%5E3%E2%88%9A((3t%5E2)%5E2+%2B+(2t)%5E2))+dt