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 ( 3 x + 1 ) 2 d x . Find the limit of the given improper integral to check whether it is convergent or divergent. ∫ 0 ∞ 1 ( 3 x + 1 ) 2 d x = lim b → ∞ ∫ 0 b 1 ( 3 x + 1 ) 2 d x = − 1 3 lim b → ∞ [ 1 3 x + 1 ] 0 b

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

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

Publisher: Pearson Education

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Chapter 8, Problem 40RE

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To find: The value of the improper integral ∫0∞1(3x+1)2dx , if it is convergent.

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Chapter 8, Problem 39RE

Chapter 8, Problem 41RE

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Calculus with Applications Books a la Carte Edition

Ch. 8.1 - YOUR TURN 1 Find Ch. 8.1 - YOUR TURN 2 Find Ch. 8.1 - YOUR TURN 3 Find Ch. 8.1 - YOUR TURN 4 Find . Ch. 8.1 - YOUR TURN 5 Find Ch. 8.1 - Prob. 1WE Ch. 8.1 - Find the following. W2. Ch. 8.1 - Find the following. W3. Ch. 8.1 - Find the following. W4. Ch. 8.1 - Use integration by parts to find the integrals in...

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The value of the improper integral ∫ 0 ∞ 1 ( 3 x + 1 ) 2 d x , if it is convergent.

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To find: The value of the improper integral ∫0∞1(3x+1)2dx , if it is convergent.

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Chapter 8 Solutions