   Chapter 6.3, Problem 45E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Medicine A body assimilates a 12-hour cold tablet at a rate modeled by d C / d t = 8 − ln ( t 2 − 2 t + 4 ) , 0 ≤ t ≤ 12 , where dC/dt is measured in milligrams per hour and t is the time in hours. Use Simpson’s Rule with n = 8 to estimate the total amount of the drug absorbed into the body during the 12 hours.

To determine

To calculate: The total amount of the drug absorbed into the body during the 12 hrs using Simpson’s rule with n=8, if a body assimilates a 12-hr cold tablet at a rate modeled by dC/dt=8ln(t22t+4),0t12.

Explanation

Given Information:

A body assimilates a 12-hr cold tablet at a rate modeled by,

dC/dt=8ln(t22t+4),0t12

Where, dC/dt is measured in milligrams per hour and t is the time in hours.

Formula used:

Simpson’s Rule:

If f is continuous on [a,b] and n is an even integer, then

abf(x)dx,n=(ba3n)[f(x0)+4f(x1)+2f(x2)+4f(x3)++4f(xn1)+f(xn)].

Calculation:

Consider the definite integral as,

dC/dt=8ln(t22t+4),0t12

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