Find the surface area of solid generated by the revolution of curve x =acos^3t,y=sin^3t about x-axis
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Answer:
x=acos
3
t
∴
dt
dx
=−3acos
2
tsint, y=asin
3
t
∴
dt
dx
=+3asin
2
tcost
The closed curve is traced as t varies from 0 to 2π
∴ x
dt
dy
−y
dt
dx
=3absin
2
tcos
2
t (A)
∴ Required area =
2
1
∫
0
2π
(x
dt
dy
−y
dt
dx
)dt
=
2
3ab
∫
0
2π
sin
2
tcos
2
tdt
=
2
3ab
×4∫
0
π/2
sin
2
tcos
2
tdt
=
2
3ab
×4×
4×2
1×1
×
2
π
( Using Wallis formula).
=
8
3abπ
Hope this will help you
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