Evaluate the following integral. dx √√x². + 2x + 122 What trigonometric substitution will be the most helpful for evaluating this integral? O A. x+1= 11 sin 0 OB. x+1=11 tan 0 C. x+1=11 sec 0 Rewrite the integrand by completing the square. Do not perform a substitution. dx S S √√x²+2x+122 (Type an exact answer, using radicals as needed. Type an expression using x as the variable.) Use this substitution to rewrite the integral found by completing the square. dx S + 2x + 122 (Type an exact answer, using radicals as needed. Type an expression using as the variable.) Evaluate the indefinite integral. dx S- √x². = = + 2x + 122 (Type an exact answer.) dx de
Evaluate the following integral. dx √√x². + 2x + 122 What trigonometric substitution will be the most helpful for evaluating this integral? O A. x+1= 11 sin 0 OB. x+1=11 tan 0 C. x+1=11 sec 0 Rewrite the integrand by completing the square. Do not perform a substitution. dx S S √√x²+2x+122 (Type an exact answer, using radicals as needed. Type an expression using x as the variable.) Use this substitution to rewrite the integral found by completing the square. dx S + 2x + 122 (Type an exact answer, using radicals as needed. Type an expression using as the variable.) Evaluate the indefinite integral. dx S- √x². = = + 2x + 122 (Type an exact answer.) dx 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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Question
![**Evaluate the following integral.**
\[
\int \frac{dx}{\sqrt{x^2 + 2x + 122}}
\]
---
**What trigonometric substitution will be the most helpful for evaluating this integral?**
- **A.** \( x + 1 = 11 \sin \theta \)
- **B.** \( x + 1 = 11 \tan \theta \)
- **C.** \( x + 1 = 11 \sec \theta \)
---
**Rewrite the integrand by completing the square. Do not perform a substitution.**
\[
\int \frac{dx}{\sqrt{x^2 + 2x + 122}} = \int \frac{dx}{(\text{[Box for answer]})}
\]
*(Type an exact answer, using radicals as needed. Type an expression using \( x \) as the variable.)*
---
**Use this substitution to rewrite the integral found by completing the square.**
\[
\int \frac{dx}{\sqrt{x^2 + 2x + 122}} = \int \frac{d\theta}{(\text{[Box for answer]})}
\]
*(Type an exact answer, using radicals as needed. Type an expression using \( \theta \) as the variable.)*
---
**Evaluate the indefinite integral.**
\[
\int \frac{dx}{\sqrt{x^2 + 2x + 122}} = \text{[Box for answer]}
\]
*(Type an exact answer.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8288b48-397c-47a1-92e8-4d9421f21f30%2F01b33350-62fe-40ec-83e3-fd7deee5c328%2Fw4eo41r_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the following integral.**
\[
\int \frac{dx}{\sqrt{x^2 + 2x + 122}}
\]
---
**What trigonometric substitution will be the most helpful for evaluating this integral?**
- **A.** \( x + 1 = 11 \sin \theta \)
- **B.** \( x + 1 = 11 \tan \theta \)
- **C.** \( x + 1 = 11 \sec \theta \)
---
**Rewrite the integrand by completing the square. Do not perform a substitution.**
\[
\int \frac{dx}{\sqrt{x^2 + 2x + 122}} = \int \frac{dx}{(\text{[Box for answer]})}
\]
*(Type an exact answer, using radicals as needed. Type an expression using \( x \) as the variable.)*
---
**Use this substitution to rewrite the integral found by completing the square.**
\[
\int \frac{dx}{\sqrt{x^2 + 2x + 122}} = \int \frac{d\theta}{(\text{[Box for answer]})}
\]
*(Type an exact answer, using radicals as needed. Type an expression using \( \theta \) as the variable.)*
---
**Evaluate the indefinite integral.**
\[
\int \frac{dx}{\sqrt{x^2 + 2x + 122}} = \text{[Box for answer]}
\]
*(Type an exact answer.)*
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