Explanation Given: The integral: I = ∫ 0 1 d x x ( 2 x + 5 ) Formula used: I = ∫ a b f ( x ) d x = [ F ( x ) ] a b = F ( b ) − F ( a ) I = ∫ a b f ( x ) d x = ∫ a c 1 f ( x ) d x + ∫ c 1 c 2 f ( x ) d x + ... + ∫ c n − 1 b f ( x ) d x , Where a < c 1 < c 2 < ... < c n − 1 < b Calculation: The integral we have I = ∫ 0 1 d x x ( 2 x + 5 ) Assume, 1 x ( 2 x + 5 ) = A x + B ( 2 x + 5 ) Now, A = lim x → 0 x [ 1 x ( 2 x + 5 ) ] = lim x → 0 [ 1 ( 2 x + 5 ) ] = [ 1 ( 2 × 0 + 5 ) ] = 1 5 B = lim x → − 5 2 ( 2 x + 5 ) [ 1 x ( 2 x + 5 ) ] = lim x → − 5 2 [ 1 x ] = [ 1 − 5 2 ] = − 2 5 ∴ 1 x ( 2 x + 5 ) = A x + B ( 2 x + 5 ) = 1 5 x + − 2 5 ( 2 x + 5 ) (1) I = ∫ 0 1 d x x ( 2 x + 5 )

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

Videos

Question

Chapter 8.7, Problem 43E

To determine

The value of the integral

$I = \int_{0}^{1} \frac{d x}{x (2 x + 5)}$

Whether the given integral is convergent or divergent.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.7, Problem 42E

Chapter 8.7, Problem 44E

Chapter 8 Solutions

Calculus - Standalone book

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The value of the integral I = ∫ 0 1 d x x ( 2 x + 5 ) Whether the given integral is convergent or divergent.

Solution Summary: The author explains that the integral is convergent or divergent.

Concept explainers

Videos

The value of the integral

$I = \int_{0}^{1} \frac{d x}{x (2 x + 5)}$

Whether the given integral is convergent or divergent.

Want to see the full answer?

Chapter 8 Solutions

The value of the integral I = ∫ 0 1 d x x ( 2 x + 5 ) Whether the given integral is convergent or divergent.

Solution Summary: The author explains that the integral is convergent or divergent.

Concept explainers

Videos

The value of the integral I=∫01dxx(2x+5) Whether the given integral is convergent or divergent.

Want to see the full answer?

Chapter 8 Solutions

The value of the integral

$I = \int_{0}^{1} \frac{d x}{x (2 x + 5)}$

Whether the given integral is convergent or divergent.