Explanation Definition used: Improper integral: “If f is continuous on [ a , ∞ ) , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . If it exists and finite, then it is converges otherwise diverges”. Theorem used: Fundamental Theorem: “Let f be a continuous function on [ a , b ] . If F is anti-derivative of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) ”. Calculation: The rate of toxic chemicals per years is given by R ( t ) = 500 ( 1 + t ) 2 . In order to find total amount of toxic chemicals, its enough to integrate the expression R ( t ) = 500 ( 1 + t ) 2 over the interval [ 0 , ∞ ) . That is, ∫ 0 ∞ 500 ( 1 + t ) 2 d t . Compute the integral ∫ 0 ∞ 500 ( 1 + t ) 2 d t by using above definition and theorem

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

See similar textbooks

Concept explainers

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

Videos

Question

Chapter 11.1, Problem 69E

To determine

To find: The total amount of toxic chemicals that seep from the dump.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 68E

Chapter 11.1, Problem 70E

Students have asked these similar questions

5. Find the average rate of growth of the function f(r) = x² + 2x + 3 from x = -5 to r= -3.

2. Two people on scooters just finished their conversation. One of them starts riding directly north at a rate of 15 m/sec. Twenty seconds later the second starts to ride directly east at a rate of 12 m/sec. At what rate is the distance between the two people increasing 30 seconds after the second person started moving? Include a labeled picture, with variables and constants clearly noted, and all work clearly shown.

4. Suppose that antibiotics are injected into a patient to treat a sinus infec- tion. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. e-at – e-ßt C(t) В — а where a and B are constants with ß > a > 0. (a) occurs. (Your argument must use the first derivative test.) Using the first derivative test, find when the maximum concentration (b) (Your answer should be supported by a rigorous argument.) When does the rate of change of concentration begin to increase?

Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The total amount of toxic chemicals that seep from the dump.

Solution Summary: The author explains that the total amount of toxic chemicals seeped from the dump is 500 gallons. If F is anti-derivative of f, it is converges otherwise diverges.

Concept explainers

Videos

To find: The total amount of toxic chemicals that seep from the dump.

Want to see the full answer?

Chapter 11 Solutions