Chapter 5: Q. 34 (page 478)

Use limits of definite integrals to calculate each of the improper integrals in Exercises.
$\int_{4}^{\infty} \frac{2 x - 4}{x^{2} - 4 x + 3} d x$

Short Answer

Expert verified

The improper integral on $[4, \infty)$ diverges.

$\int_{4}^{\infty} \frac{2 x - 4}{x^{2} - 4 x + 3} d x = \infty$

Step by step solution

Step 1. Given information.

The given integral is the following.

$\int_{4}^{\infty} \frac{2 x - 4}{x^{2} - 4 x + 3} d x$

Step 2. Value of integral.

Find the integral value.

$\int_{4}^{\infty} \frac{2 x - 4}{x^{2} - 4 x + 3} d x = \lim_{b \to \infty} \int_{4}^{b} \frac{2 x - 4}{x^{2} - 4 x + 3} d x = \lim_{b \to \infty} {[\ln |x^{2} - 4 x + 3|]}_{4}^{b} = \lim_{b \to \infty} (\ln |b^{2} - 4 b + 3| - \ln 3) = \infty - \ln 3 = \infty$

So integral on $[4, \infty)$ diverges

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Use limits of definite integrals to calculate each of the improper integrals in Exercises.
$\int_{4}^{\infty} \frac{2 x - 4}{x^{2} - 4 x + 3} d x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of integral.

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Use limits of definite integrals to calculate each of the improper integrals in Exercises.∫4∞2x-4x2-4x+3dx

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of integral.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Calculus

Geometry

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Use limits of definite integrals to calculate each of the improper integrals in Exercises.
$\int_{4}^{\infty} \frac{2 x - 4}{x^{2} - 4 x + 3} d x$