Suppose an oral dose of a drug is taken. Over, time, the drug is assimilated in the body and excreted though the urine. The total amount of the drug that has passed through the body in T hours is given by ∫ 0 T E ( t ) d t , where E ( t ) is the rate of excretion of the drug. A typical rate-of-excretion function is E ( t ) = t e − k t , where k > 0 and t is the time, in hours. Use this information for Exercises 49-50. Find ∫ 0 ∞ E ( t ) d t , and interpret the answer. That is, what does the integral represent?
Suppose an oral dose of a drug is taken. Over, time, the drug is assimilated in the body and excreted though the urine. The total amount of the drug that has passed through the body in T hours is given by ∫ 0 T E ( t ) d t , where E ( t ) is the rate of excretion of the drug. A typical rate-of-excretion function is E ( t ) = t e − k t , where k > 0 and t is the time, in hours. Use this information for Exercises 49-50. Find ∫ 0 ∞ E ( t ) d t , and interpret the answer. That is, what does the integral represent?
Solution Summary: The author explains how to calculate the value of displaystyle, in the equation, and interpret the answer.
Suppose an oral dose of a drug is taken. Over, time, the drug is assimilated in the body and excreted though the urine. The total amount of the drug that has passed through the body in T hours is given by
∫
0
T
E
(
t
)
d
t
,
where
E
(
t
)
is the rate of excretion of the drug. A typical rate-of-excretion function is
E
(
t
)
=
t
e
−
k
t
,
where
k
>
0
and t is the time, in hours. Use this information for Exercises 49-50.
Find
∫
0
∞
E
(
t
)
d
t
,
and interpret the answer. That is, what does the integral represent?
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
University Calculus: Early Transcendentals (3rd Edition)
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