Apply the trigonometric substitution x = √3 sec(0). When determining the lower limit, you will have two possible choices for 0. Pick the value of that has its terminal side in the quadrant that ensures √x² - 3 will be positive. -√3 6x²-3 dx = X 6√3 sec²(0) - 3 √3 sec(0) X X ) de
Apply the trigonometric substitution x = √3 sec(0). When determining the lower limit, you will have two possible choices for 0. Pick the value of that has its terminal side in the quadrant that ensures √x² - 3 will be positive. -√3 6x²-3 dx = X 6√3 sec²(0) - 3 √3 sec(0) X X ) de
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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![Apply the trigonometric substitution \( x = \sqrt{3} \sec(\theta) \). When determining the lower limit, you will have two possible choices for \( \theta \). Pick the value of \( \theta \) that has its terminal side in the quadrant that ensures \( \sqrt{x^2 - 3} \) will be positive.
\[
\int_{-2}^{-\sqrt{3}} \frac{6 \sqrt{x^2 - 3}}{x} \, dx = \int_{\Box}^{\pi} \frac{6 \sqrt{3 \sec^2(\theta) - 3}}{\sqrt{3} \sec(\theta)} \, \Box \, d\theta
\]
\[
= \int_{\Box}^{\pi} (\Box) \, d\theta
\]
Note: Each box represents a missing value or expression to be determined in the process of trigonometric substitution and integration.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcdc0c33c-1cee-4754-904a-1b31674d8af7%2F3a266e14-4a79-4256-a77b-830e2d3a4f7b%2Fwixm5zd_processed.png&w=3840&q=75)
Transcribed Image Text:Apply the trigonometric substitution \( x = \sqrt{3} \sec(\theta) \). When determining the lower limit, you will have two possible choices for \( \theta \). Pick the value of \( \theta \) that has its terminal side in the quadrant that ensures \( \sqrt{x^2 - 3} \) will be positive.
\[
\int_{-2}^{-\sqrt{3}} \frac{6 \sqrt{x^2 - 3}}{x} \, dx = \int_{\Box}^{\pi} \frac{6 \sqrt{3 \sec^2(\theta) - 3}}{\sqrt{3} \sec(\theta)} \, \Box \, d\theta
\]
\[
= \int_{\Box}^{\pi} (\Box) \, d\theta
\]
Note: Each box represents a missing value or expression to be determined in the process of trigonometric substitution and integration.
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