Chapter 8: Q. 66 (page 702)

Use the results from Exercises 51–60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61–70 to within 0.001 of their values.
$\int_{0.5}^{1} \ln (4 + x^{2}) dx$

Short Answer

Expert verified

$\int_{0.5}^{1} \ln (4 + x^{2}) dx \approx 0.761$

Step by step solution

Step 1. Given information is:

$\int_{0.5}^{1} \ln (4 + x^{2}) dx$

Step 2. Approximating the values

$From Q 55 . \int_{0.5}^{1} \ln (4 + x^{2}) dx = \frac{(\ln 4)}{2} + \sum_{k = 1}^{\infty} \frac{{(- 1)}^{k + 1}}{k . 2^{2 k}} \frac{(1 - 0 . 5^{2 k + 1})}{2 k + 1} This implies that to approximate the values of integrals, put the value of k \int_{0.5}^{1} \ln (4 + x^{2}) dx = 0.693147 + \frac{0.875}{4 \cdot 3} - \frac{0.96875}{2 \cdot 16 \cdot 5} + . . . = 0.693147 + 0.0729 - 0.00605 + . . . \approx 0.761$

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Use the results from Exercises 51–60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61–70 to within 0.001 of their values.
$\int_{0.5}^{1} \ln (4 + x^{2}) dx$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Approximating the values

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Use the results from Exercises 51–60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61–70 to within 0.001 of their values.∫0.51ln(4+x2)dx

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Approximating the values

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Use the results from Exercises 51–60 and Theorem 7.38 to approximate the values of the definite integrals in Exercises 61–70 to within 0.001 of their values.
$\int_{0.5}^{1} \ln (4 + x^{2}) dx$