The capitalized cost is .
Here ,
and
.
(a)
\Find the capitalized cost for years.
Substitute ,
and
and
in
.
Consider .
Solve the integral by using integration by parts.
Formula for integration by parts : .
Here and
.
Consider .
Apply derivative on each side with respect to .
.
Consider .
Integrate on each side.
\.
Substitute corresponding values.
\Substitute .
Therefore, the capitalized cost for years is
.
(b)
\The capitalized cost is .
Find the capitalized cost for years.
Substitute ,
and
and
in
.
.
Substitute
Therefore, the capitalized cost for years is
.
(c)
\The capitalized cost is .
Find the capitalized cost for forever.
\Substitute ,
,
and
in
.
Substitute .
Therefore, the capitalized cost for forever is .
(a) The capitalized cost for years is
.
(b) The capitalized cost for years is
.
(c) The capitalized cost for forever is .