Explanation 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 integral is F ( b ) = ∫ 1 b x 2 d x . Use above theorem to calculate the given integral. F ( b ) = ∫ 1 b 1 x 4 d x = [ x − 4 + 1 − 4 + 1 ] 1 b = − [ 1 3 x 3 ] 1 b = − 1 3 [

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Chapter 11.1, Problem 42E

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To sketch: The graph of F(b)=∫1b1x4dx and estimate limb→∞F(b) using graph.

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Chapter 11.1, Problem 41E

Chapter 11.1, Problem 43E

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Chapter 11 Solutions

EP CALCULUS F/BUS.,ECON.-BRIEF-ACCESS

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 graph of F ( b ) = ∫ 1 b 1 x 4 d x and estimate lim b → ∞ F ( b ) using graph.

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To sketch: The graph of F(b)=∫1b1x4dx and estimate limb→∞F(b) using graph.

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Chapter 11 Solutions