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, ∫ − ∞ − 4 3 x 4 d x . The integrand f ( x ) = 3 x 4 is finite on the unbounded interval ( − ∞ , − 4 ] . Find the limit of the given improper integral to check whether it is convergent or divergent

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Chapter 8.4, Problem 6E

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To find: The value of the improper integral ∫−∞−43x4dx , if it is convergent.

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Chapter 8.4, Problem 5E

Chapter 8.4, Problem 7E

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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 ∫ − ∞ − 4 3 x 4 d x , if it is convergent.

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To find: The value of the improper integral ∫−∞−43x4dx , if it is convergent.

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Chapter 8 Solutions