6 dx. 1+ 9x2 Calculate

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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To calculate the integral \(\int_{1}^{2} \frac{6}{1 + 9x^2} \, dx\). 

Follow these steps:

1. **Identify the Integral Form**:
   Recognize that this is a standard form integral typically involving a trigonometric substitution.

2. **Apply Trigonometric Substitution**:
   Use a substitution to simplify the integrand if necessary.

3. **Integrate**:
   Perform the integration by recognizing or transforming the integrand into a known form.

4. **Evaluate the Definite Integral**:
   Substitute the upper and lower limits of the integral to find the exact numerical value.

Let's breakdown the procedure further to solve this integral.

To learn more, proceed with integration techniques and rules for trigonometric substitutions explained in detail in following sections.
Transcribed Image Text:To calculate the integral \(\int_{1}^{2} \frac{6}{1 + 9x^2} \, dx\). Follow these steps: 1. **Identify the Integral Form**: Recognize that this is a standard form integral typically involving a trigonometric substitution. 2. **Apply Trigonometric Substitution**: Use a substitution to simplify the integrand if necessary. 3. **Integrate**: Perform the integration by recognizing or transforming the integrand into a known form. 4. **Evaluate the Definite Integral**: Substitute the upper and lower limits of the integral to find the exact numerical value. Let's breakdown the procedure further to solve this integral. To learn more, proceed with integration techniques and rules for trigonometric substitutions explained in detail in following sections.
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