Solutions Calculus

After a certain pathogen enters the bloodstream, the rate at which antibodies are made as a function

Question: After a certain pathogen enters the bloodstream, the rate at which antibodies are made as a function of time in minutes is given by

\[R\left( t \right)=\frac{1000t}{{{t}^{2}}+1}\]

a) Write a definite integral expressing the change in the number of antibodies in the blood at the end of 4 minutes.

b) Use the right-hand sum in 2 to estimate this number. Explain why this gives a better estimate than the left-hand sum in this case.

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