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Calculus / Thomas' Calculus: Early Transcendentals 13 / Chapter 8.8 / Problem 20E

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

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Evaluating Improper IntegralsEvaluate the

Chapter 8, Problem 20E

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QUESTION:

Problem 20E

Evaluating Improper Integrals

Evaluate the integrals without using tables.

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QUESTION:

Problem 20E

Evaluating Improper Integrals

Evaluate the integrals without using tables.

ANSWER:

Solution:

Step 1 of 3:

In this problem, we have to evaluate the integral

Step 1 of 3: $\$

We gave the integral $\int\limits_{0}^{\infty{}}\frac{16\ ta{n}^{-1}x}{1\ +\ {x}^{2}}\ dx$

We have the function which is lie between $x\ =0\ to\ x\ =b$ and examine the limit as $b\rightarrow{}\infty{}.$

That is $\int\limits_{0}^{\infty{}}\frac{16\ ta{n}^{-1}x}{1\ +\ {x}^{2}}\ dx=\lim\limits_{{b\ } \rightarrow {\infty{}}}\ \ \int\limits_{0}^{b}\frac{16\ ta{n}^{-1}x}{1\ +\ {x}^{2}}$

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