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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Complete the square before using trigonometric substitution
![### Integral Problem
**Problem 49: Evaluate the Integral**
\[ \int \sqrt{8 - 2x - x^2} \, dx \]
In this problem, you are asked to evaluate the integral of the function \( \sqrt{8 - 2x - x^2} \) with respect to \( x \). This involves finding an antiderivative for the given function under the square root. The problem is taken from a calculus topic involving techniques of integration, particularly focusing on integrals that may require completing the square or trigonometric substitution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf95109c-869d-4f91-a635-386ab8bbffdb%2Fe0d3a910-4a1e-4563-b622-6263bc24a958%2Fozkhgdv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Integral Problem
**Problem 49: Evaluate the Integral**
\[ \int \sqrt{8 - 2x - x^2} \, dx \]
In this problem, you are asked to evaluate the integral of the function \( \sqrt{8 - 2x - x^2} \) with respect to \( x \). This involves finding an antiderivative for the given function under the square root. The problem is taken from a calculus topic involving techniques of integration, particularly focusing on integrals that may require completing the square or trigonometric substitution.
Transcribed Image Text:**Complete the Square Before Using Trigonometric Substitutions**
For Exercises 49–52, complete the square before using an appropriate trigonometric substitution.
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