Explanation Consider the function f ( x ) = { 4 ( x + 1 ) 2 if x ≥ 1 0 otherwise . Sketch the graph of the function y = f ( x ) is as shown below in Figure 1. From Figure 1, it is observed that the function is discontinues at x = 1 . Simplify the improper integral ∫ − ∞ ∞ f ( x ) d x to obtain the value as follows. ∫ − ∞ ∞ f ( x ) d x = ∫ − ∞ 1 f ( x ) d x + ∫ 1 ∞ f ( x ) d x = ∫ − ∞ 1 0 d x + ∫ 1 ∞

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Author: Stocker

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 11.1, Problem 34E

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To sketch: The graph of the function y=f(x) and compute the value of the improper integral ∫−∞∞f(x)dx that converges.

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Chapter 11.1, Problem 33E

Chapter 11.1, Problem 35E

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EBK CALCULUS FOR BUSINESS, ECONOMICS, L

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 the function y = f ( x ) and compute the value of the improper integral ∫ − ∞ ∞ f ( x ) d x that converges.

Solution Summary: The author illustrates the graph of the function y=f(x).

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To sketch: The graph of the function y=f(x) and compute the value of the improper integral ∫−∞∞f(x)dx that converges.

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