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| PAGE: 476 | SET: Exercises | PROBLEM: 61 |
The function is 
.
Observe the graph :
Let 
be the region bounded by the function 
, the 
axis, 
and 
.
Where 
.
Let 
be the solid formed when 
is revolved around axis.
(a)
.
Differentiate with respective to 
.
Volume can be calculated by the formula 
.
Where 
is 
.
(b)
Definition Of Arc Length :
Let the function given by 
represent a smooth curve on the interval 
.
The surface area of 
between 
and 
is 
.
Where is 
.
(c)
Observe the graph :
.
.
(d)
In the above function :
on the interval 
.
Now we have 
.
In the step 3 :
. So,
.
Which is the surface area 
.
Therefore 
as 
.
(a)
The volume 
is 
.
(b)
The surface area is 
.
(c)
.
(d)
.
as 
.
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