Explanation Definition used: Improper integral Let a function f is continuous on the unbounded interval [ a , ∞ ) . Then the improper integral of f over [ a , ∞ ) is defined as ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . If it exists and is 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 k e − x k d x , where k is constant. The integrand f ( x ) = 1 k e − x k is finite on the unbounded interval [ 0 , ∞ ) . Use the definition and theorem mentioned above to check convergence of the improper integral

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Chapter 11.1, Problem 51E

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To find: The value of improper integral ∫0∞1ke−xkdx, if it converges.

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Chapter 11.1, Problem 50E

Chapter 11.1, Problem 52E

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CALCULUS FOR BUSINESS...-MYLAB ACESS

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

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The value of improper integral ∫ 0 ∞ 1 k e − x k d x , if it converges.

Solution Summary: The author calculates the value of the improper integral, if it converges. If it exists and is finite, then it is divergent.

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To find: The value of improper integral ∫0∞1ke−xkdx, if it converges.

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Chapter 11 Solutions