Explanation Definition used: Improper integral: “If f is continuous on ( − ∞ , b ] , then ∫ − ∞ b f ( x ) d x = lim a → − ∞ ∫ 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 ∫ − ∞ − 27 x − 5 3 d x . The integrand f ( x ) = x − 5 3 is finite on the unbounded interval ( − ∞ , − 27 ] . Find the limit of the given improper integral to check whether it is convergent or divergent. ∫ − ∞ − 27 x − 5 3 d x = lim a → − ∞ ∫ − ∞ − 27 x − 5 3 d x = − 3 2 lim a → − ∞ [ 1 x 2 3

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 Integral

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Chapter 16.4, Problem 12E

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To find: The value of the improper integral ∫−∞−27x−53dx , if it is convergent.

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Chapter 16.4, Problem 11E

Chapter 16.4, Problem 13E

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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...

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The value of the improper integral ∫ − ∞ − 27 x − 5 3 d x , if it is convergent.

Solution Summary: The author explains that the improper integral is convergent and its value is -16.

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To find: The value of the improper integral ∫−∞−27x−53dx , if it is convergent.

Want to see the full answer?

Chapter 16 Solutions