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 is exist and finite, then it is convergent otherwise divergent.” 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 given improper integral is ∫ 0 ∞ 1 ( 4 x + 1 ) 3 d x . Find the limit of the given improper integral to check whether it is convergent or divergent. ∫ 0 ∞ 1 ( 4 x + 1 ) 3 d x = lim b → ∞ ∫ 0 b 1 ( 4 x + 1 ) 3 d x = − 1 8 lim b → ∞ [ 1 ( 4 x + 1 ) 2 ] 0 b = − 1 8 lim

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Chapter 16.4, Problem 20E

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To find: The value of the improper integral ∫0∞1(4x+1)3dx , if it is convergent.

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Chapter 16.4, Problem 19E

Chapter 16.4, Problem 21E

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Chapter 16 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 16.1 - Find xe2xdx.Ch. 16.1 - Find ln2xdx.Ch. 16.1 - Prob. 3YT Ch. 16.1 - Find 1ex2lnxdx.Ch. 16.1 - Prob. 5YT Ch. 16.1 - Prob. 1WE Ch. 16.1 - Find the following. W2.(3x52x3)dx Ch. 16.1 - Find the following. W3.(x23+1x)dx Ch. 16.1 - Prob. 4WE Ch. 16.1 - Use integration by parts to find the integrals in...

Ch. 16.1 - Prob. 6WE Ch. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Use integration by parts to find the integrals in...Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Exercises 1322 are mixedsome require integration...Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - What rule of differentiation is related to...Ch. 16.1 - Prob. 30E Ch. 16.1 - Suppose that u and v are differentiable functions...Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.2 - Prob. 1YT Ch. 16.2 - Prob. 2YT Ch. 16.2 - Prob. 1WE Ch. 16.2 - Prob. 2WE Ch. 16.2 - Prob. 3WE Ch. 16.2 - Prob. 4WE Ch. 16.2 - Prob. 5WE Ch. 16.2 - Prob. 6WE Ch. 16.2 - Prob. 1E Ch. 16.2 - Prob. 2E Ch. 16.2 - Prob. 3E Ch. 16.2 - Prob. 4E Ch. 16.2 - Prob. 5E Ch. 16.2 - Prob. 6E Ch. 16.2 - Prob. 7E Ch. 16.2 - Prob. 8E Ch. 16.2 - Prob. 9E Ch. 16.2 - Prob. 10E Ch. 16.2 - Prob. 11E Ch. 16.2 - Prob. 12E Ch. 16.2 - Prob. 13E Ch. 16.2 - Prob. 14E Ch. 16.2 - Prob. 15E Ch. 16.2 - Prob. 16E Ch. 16.2 - Prob. 17E Ch. 16.2 - Prob. 18E Ch. 16.2 - Prob. 19E Ch. 16.2 - Prob. 20E Ch. 16.2 - Prob. 21E Ch. 16.2 - Prob. 22E Ch. 16.2 - Prob. 23E Ch. 16.2 - Prob. 24E Ch. 16.2 - Prob. 25E Ch. 16.2 - Prob. 26E Ch. 16.2 - Prob. 27E Ch. 16.2 - Prob. 28E Ch. 16.2 - Prob. 29E Ch. 16.2 - Prob. 30E Ch. 16.2 - Prob. 31E Ch. 16.2 - Prob. 32E Ch. 16.2 - Prob. 33E Ch. 16.2 - Prob. 34E Ch. 16.2 - Prob. 35E Ch. 16.2 - Prob. 36E Ch. 16.2 - Prob. 37E Ch. 16.2 - Prob. 38E Ch. 16.2 - Prob. 39E Ch. 16.2 - Prob. 40E Ch. 16.2 - Prob. 41E Ch. 16.2 - Prob. 42E Ch. 16.2 - Prob. 43E Ch. 16.2 - Typing Speed The function W(t)=3.75t2+30t+40...Ch. 16.2 - Prob. 45E Ch. 16.3 - Prob. 1YT Ch. 16.3 - Prob. 2YT Ch. 16.3 - Prob. 3YT Ch. 16.3 - Prob. 4YT Ch. 16.3 - Prob. 1WE Ch. 16.3 - Prob. 2WE Ch. 16.3 - Prob. 3WE Ch. 16.3 - Prob. 4WE Ch. 16.3 - Each of the functions in Exercises 114 represents...Ch. 16.3 - Prob. 2E Ch. 16.3 - Prob. 3E Ch. 16.3 - Prob. 4E Ch. 16.3 - Prob. 5E Ch. 16.3 - Each of the functions in Exercises 114 represents...Ch. 16.3 - Prob. 7E Ch. 16.3 - Prob. 8E Ch. 16.3 - Each of the functions in Exercises 114 represents...Ch. 16.3 - Prob. 10E Ch. 16.3 - Prob. 11E Ch. 16.3 - Prob. 12E Ch. 16.3 - Prob. 13E Ch. 16.3 - Prob. 14E Ch. 16.3 - Prob. 15E Ch. 16.3 - Prob. 16E Ch. 16.3 - Prob. 17E Ch. 16.3 - Prob. 18E Ch. 16.3 - Present Value A money market fund has a continuous...Ch. 16.3 - Accumulated Amount of Money Flow Find the amount...Ch. 16.4 - Prob. 1YT Ch. 16.4 - Prob. 2YT Ch. 16.4 - Prob. 1WE Ch. 16.4 - Prob. 2WE Ch. 16.4 - Prob. 3WE Ch. 16.4 - Prob. 4WE Ch. 16.4 - Prob. 1E Ch. 16.4 - Prob. 2E Ch. 16.4 - Prob. 3E Ch. 16.4 - Prob. 4E Ch. 16.4 - Prob. 5E Ch. 16.4 - Prob. 6E Ch. 16.4 - Prob. 7E Ch. 16.4 - Prob. 8E Ch. 16.4 - Prob. 9E Ch. 16.4 - Prob. 10E Ch. 16.4 - Prob. 11E Ch. 16.4 - Prob. 12E Ch. 16.4 - Prob. 13E Ch. 16.4 - Prob. 14E Ch. 16.4 - Prob. 15E Ch. 16.4 - Prob. 16E Ch. 16.4 - Prob. 17E Ch. 16.4 - Prob. 18E Ch. 16.4 - Prob. 19E Ch. 16.4 - Prob. 20E Ch. 16.4 - Prob. 21E Ch. 16.4 - Prob. 22E Ch. 16.4 - Prob. 23E Ch. 16.4 - Prob. 24E Ch. 16.4 - Determine whether each improper integral converges...Ch. 16.4 - Prob. 26E Ch. 16.4 - Prob. 27E Ch. 16.4 - Prob. 28E Ch. 16.4 - Determine whether each improper integral converges...Ch. 16.4 - Prob. 30E Ch. 16.4 - Prob. 31E Ch. 16.4 - Prob. 32E Ch. 16.4 - Prob. 33E Ch. 16.4 - Prob. 34E Ch. 16.4 - Prob. 35E Ch. 16.4 - Prob. 36E Ch. 16.4 - Prob. 37E Ch. 16.4 - Prob. 38E Ch. 16.4 - Prob. 39E Ch. 16.4 - Prob. 40E Ch. 16.4 - Prob. 41E Ch. 16.4 - Prob. 42E Ch. 16.4 - Prob. 43E Ch. 16.4 - Prob. 44E Ch. 16.4 - Prob. 45E Ch. 16.4 - Prob. 46E Ch. 16.4 - Prob. 47E Ch. 16.4 - Prob. 48E Ch. 16.4 - Prob. 49E Ch. 16.4 - Prob. 50E Ch. 16.4 - Prob. 51E Ch. 16.4 - Prob. 52E Ch. 16.4 - Radioactive Waste The rate at which radioactive...Ch. 16.4 - Prob. 54E Ch. 16.5 - Find all solutions of the differential equation...Ch. 16.5 - Prob. 2YT Ch. 16.5 - Prob. 3YT Ch. 16.5 - In Example 6, find the goat population in 5 years...Ch. 16.5 - Prob. 1WE Ch. 16.5 - Prob. 2WE Ch. 16.5 - Prob. 3WE Ch. 16.5 - Prob. 4WE Ch. 16.5 - Prob. 5WE Ch. 16.5 - Prob. 1E Ch. 16.5 - Prob. 2E Ch. 16.5 - Prob. 3E Ch. 16.5 - Prob. 4E Ch. 16.5 - Prob. 5E Ch. 16.5 - Prob. 6E Ch. 16.5 - Prob. 7E Ch. 16.5 - Prob. 8E Ch. 16.5 - Prob. 9E Ch. 16.5 - Prob. 10E Ch. 16.5 - Prob. 11E Ch. 16.5 - Prob. 12E Ch. 16.5 - Prob. 13E Ch. 16.5 - Prob. 14E Ch. 16.5 - Prob. 15E Ch. 16.5 - Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Find the particular solution for each initial...Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Find the particular solution for each initial...Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.5 - Prob. 35E Ch. 16.5 - Prob. 36E Ch. 16.5 - Suppose that 0 y0 N. Let b = (N y0)/y0, and let...Ch. 16.5 - Prob. 38E Ch. 16.5 - Prob. 39E Ch. 16.5 - Prob. 40E Ch. 16.5 - Prob. 41E Ch. 16.5 - Prob. 42E Ch. 16.5 - Prob. 43E Ch. 16.5 - Prob. 45E Ch. 16.5 - Prob. 46E Ch. 16.5 - Soil Moisture The evapotranspiration index I is a...Ch. 16.5 - Fish Population An isolated fish population is...Ch. 16.5 - Prob. 49E Ch. 16.5 - Prob. 50E Ch. 16.5 - Prob. 53E Ch. 16.5 - Prob. 54E Ch. 16.5 - Prob. 55E Ch. 16.5 - Worker Productivity A company has found that the...Ch. 16.5 - Spread of a Rumor Suppose the rate at which a...Ch. 16.5 - Prob. 59E Ch. 16.5 - Prob. 60E Ch. 16.5 - Prob. 61E Ch. 16.5 - Prob. 62E Ch. 16.5 - Prob. 63E Ch. 16.5 - Prob. 64E Ch. 16 - Determine whether each of the following statements...Ch. 16 - Determine whether each of the following statements...Ch. 16 - Determine whether each of the following statements...Ch. 16 - Prob. 4RE Ch. 16 - Determine whether each of the following statements...Ch. 16 - Determine whether each of the following statements...Ch. 16 - Determine whether each of the following statements...Ch. 16 - Prob. 8RE Ch. 16 - Prob. 9RE Ch. 16 - Prob. 10RE Ch. 16 - Prob. 11RE Ch. 16 - Prob. 12RE Ch. 16 - Prob. 13RE Ch. 16 - Prob. 14RE Ch. 16 - Prob. 15RE Ch. 16 - Compare finding the average value of a function...Ch. 16 - Prob. 17RE Ch. 16 - Prob. 18RE Ch. 16 - Prob. 19RE Ch. 16 - Prob. 20RE Ch. 16 - Prob. 21RE Ch. 16 - Prob. 22RE Ch. 16 - Prob. 23RE Ch. 16 - Prob. 24RE Ch. 16 - Prob. 25RE Ch. 16 - Prob. 26RE Ch. 16 - Find each integral, using techniques from this or...Ch. 16 - Prob. 28RE Ch. 16 - Prob. 29RE Ch. 16 - Prob. 30RE Ch. 16 - Prob. 31RE Ch. 16 - Prob. 32RE Ch. 16 - Prob. 33RE Ch. 16 - Prob. 34RE Ch. 16 - Prob. 35RE Ch. 16 - Prob. 36RE Ch. 16 - Prob. 37RE Ch. 16 - Prob. 38RE Ch. 16 - Prob. 39RE Ch. 16 - Prob. 40RE Ch. 16 - Prob. 41RE Ch. 16 - Prob. 42RE Ch. 16 - Prob. 43RE Ch. 16 - Prob. 44RE Ch. 16 - Prob. 45RE Ch. 16 - Prob. 46RE Ch. 16 - Prob. 47RE Ch. 16 - Prob. 48RE Ch. 16 - Prob. 49RE Ch. 16 - Prob. 50RE Ch. 16 - Prob. 51RE Ch. 16 - Prob. 52RE Ch. 16 - Prob. 53RE Ch. 16 - Prob. 54RE Ch. 16 - Prob. 55RE Ch. 16 - Prob. 56RE Ch. 16 - Prob. 57RE Ch. 16 - Prob. 58RE Ch. 16 - Prob. 59RE Ch. 16 - Prob. 60RE Ch. 16 - Prob. 61RE Ch. 16 - Prob. 62RE Ch. 16 - Prob. 63RE Ch. 16 - Prob. 64RE Ch. 16 - Prob. 65RE Ch. 16 - Prob. 66RE Ch. 16 - Prob. 67RE Ch. 16 - Prob. 68RE Ch. 16 - Prob. 69RE Ch. 16 - Prob. 70RE Ch. 16 - Prob. 71RE Ch. 16 - Prob. 72RE Ch. 16 - Prob. 73RE Ch. 16 - Prob. 74RE Ch. 16 - Prob. 75RE Ch. 16 - Prob. 76RE Ch. 16 - Prob. 77RE Ch. 16 - Prob. 78RE Ch. 16 - Prob. 79RE Ch. 16 - Prob. 80RE Ch. 16 - Prob. 81RE Ch. 16 - Prob. 82RE Ch. 16 - Prob. 83RE Ch. 16 - Prob. 84RE Ch. 16 - Prob. 85RE Ch. 16 - Growth of a Mite Population A population of mites...Ch. 16 - Prob. 87RE Ch. 16 - Prob. 88RE Ch. 16 - Prob. 89RE Ch. 16 - Prob. 91RE Ch. 16 - Prob. 92RE Ch. 16 - Average Temperatures Suppose the temperature...Ch. 16 - Prob. 94RE Ch. 16 - Prob. 95RE

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The value of the improper integral ∫ 0 ∞ 1 ( 4 x + 1 ) 3 d x , if it is convergent.

Solution Summary: The author explains that the improper integral is convergent and its value is 18.

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To find: The value of the improper integral ∫0∞1(4x+1)3dx , if it is convergent.

Want to see the full answer?

Chapter 16 Solutions