Find the area of the surface generated by revolving the curve x=(y^3)/(3), 0 <= y <= 5, about the y axis. The area of the surface generated by revolving the curve x=(y^3)/(3),0 <= y <= 5, about the y-axis is __ square units

Jack Ingram

Jack Ingram

Answered question

2022-10-29

Find the area of the surface generated by revolving the curve x = y 3 3 , 0 y 5, about the y axis. The area of the surface generated by revolving the curve x = y 3 3 , 0 y 5, about the y-axis is __ square units

Answer & Explanation

Shyla Maldonado

Shyla Maldonado

Beginner2022-10-30Added 15 answers

Sol:
x = y 3 3
d x d y = 1 3 3 y 2 = y 2
d s = 1 + ( d x d y ) 2 d y
= 1 + y 4 d y
Surface area of revolution
S = 2 π x d s
= 2 π 0 5 y 3 3 1 + y 4 d y
= 2 π 3 × 4 0 5 4 y 3 1 + y 4 d y
put z = 1 + y 4   a s ,   y 0 , z 1
d z = 4 y 3 d y         y 5 , z 626
π 6 1 626 z d z
= π 6 [ z 3 / 2 3 / 2 ] 626 = π 9 [ 626 3 / 2 1 ]

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