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Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. 134. s dx √4x² 2

Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. 134. s dx √4x² 2

Calculus: Early Transcendentals
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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Can you explain to me how you convert theta to arc sin for problem # 134 the answer is arc sin x/2
This page comprises mathematical problems focusing on integration and completing the square. Here's a breakdown: ### Completing the Square - Problems 131 to 133 ask the student to express each trinomial as the square of a binomial. - **131.** \( 4x^2 - 4x + 1 \) - **132.** \( 2x^2 - 8x + 3 \) - **133.** \( -x^2 - 2x + 4 \) ### Trigonometric Substitution Integration - Problems 134 to 138 provide integrals that require trigonometric substitution. The goal is to express the final answer in terms of the variable: - **134.** \( \int \frac{dx}{\sqrt{4 - x^2}} \) (Highlighted in orange) - **135.** \( \int \frac{dx}{\sqrt{x^2 - a^2}} \) - **136.** \( \int \sqrt{4 - x^2} \, dx \) - **137.** \( \int \frac{dx}{\sqrt{1 + 9x^2}} \) (Highlighted in orange) - **138.** \( \int \frac{x^2 \, dx}{\sqrt{1 - x^2}} \) ### Additional Notes - Some exercises (134, 137, 153) are highlighted in orange. This might indicate their importance or priority. - The instructions specify using the method of trigonometric substitution, highlighting the focus on this technique for integration. This content is suitable for an educational approach to mastering integration techniques involving completing squares and trigonometric substitution.
Transcribed Image Text:This page comprises mathematical problems focusing on integration and completing the square. Here's a breakdown: ### Completing the Square - Problems 131 to 133 ask the student to express each trinomial as the square of a binomial. - **131.** \( 4x^2 - 4x + 1 \) - **132.** \( 2x^2 - 8x + 3 \) - **133.** \( -x^2 - 2x + 4 \) ### Trigonometric Substitution Integration - Problems 134 to 138 provide integrals that require trigonometric substitution. The goal is to express the final answer in terms of the variable: - **134.** \( \int \frac{dx}{\sqrt{4 - x^2}} \) (Highlighted in orange) - **135.** \( \int \frac{dx}{\sqrt{x^2 - a^2}} \) - **136.** \( \int \sqrt{4 - x^2} \, dx \) - **137.** \( \int \frac{dx}{\sqrt{1 + 9x^2}} \) (Highlighted in orange) - **138.** \( \int \frac{x^2 \, dx}{\sqrt{1 - x^2}} \) ### Additional Notes - Some exercises (134, 137, 153) are highlighted in orange. This might indicate their importance or priority. - The instructions specify using the method of trigonometric substitution, highlighting the focus on this technique for integration. This content is suitable for an educational approach to mastering integration techniques involving completing squares and trigonometric substitution.
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