Evaluate the integral: (A) Which trig substitution 36 sec (0) X = X = 6 sec (0) X = 6 sin(0) ○x = 36 sin(0) 0x = 36 tan (0) 0x = 6 tan (0) dx 4x² is correct for this integral? (B) Which integral do you obtain after substituting for x and simplifying? Note: to enter 0, type the word theta. [ ᏧᎾ
Evaluate the integral: (A) Which trig substitution 36 sec (0) X = X = 6 sec (0) X = 6 sin(0) ○x = 36 sin(0) 0x = 36 tan (0) 0x = 6 tan (0) dx 4x² is correct for this integral? (B) Which integral do you obtain after substituting for x and simplifying? Note: to enter 0, type the word theta. [ ᏧᎾ
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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![**(D) What is the value of the original integral in terms of \( x \)?**
[Answer Box] + \( C \)
*Explanation*:
The image shows a mathematical question asking for the antiderivative or indefinite integral of a function with respect to \( x \). The expression is followed by a space where the answer should be written, with a "+ \( C \)" indicating the constant of integration, which is essential in indefinite integrals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F678fef96-64be-4096-a74a-c4eb0a405ee7%2F9355cf03-344c-4a5b-8359-5bae4f7b39e6%2Fxesucmr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**(D) What is the value of the original integral in terms of \( x \)?**
[Answer Box] + \( C \)
*Explanation*:
The image shows a mathematical question asking for the antiderivative or indefinite integral of a function with respect to \( x \). The expression is followed by a space where the answer should be written, with a "+ \( C \)" indicating the constant of integration, which is essential in indefinite integrals.
![**Evaluate the integral:**
\[
\int \frac{\sqrt{36-x^2}}{4x^2} \, dx
\]
**(A) Which trig substitution is correct for this integral?**
- \( \circ \; x = 36 \sec(\theta) \)
- \( \circ \; x = 6 \sec(\theta) \)
- \( \circ \; x = 6 \sin(\theta) \)
- \( \circ \; x = 36 \sin(\theta) \)
- \( \circ \; x = 36 \tan(\theta) \)
- \( \circ \; x = 6 \tan(\theta) \)
---
**(B) Which integral do you obtain after substituting for \( x \) and simplifying?**
*Note: to enter \( \theta \), type the word theta.*
\[
\int \quad d\theta
\]
---
**(C) What is the value of the above integral in terms of \( \theta \)?**
\[
\boxed{\phantom{text}}
+ C
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F678fef96-64be-4096-a74a-c4eb0a405ee7%2F9355cf03-344c-4a5b-8359-5bae4f7b39e6%2Fxcskoij_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate the integral:**
\[
\int \frac{\sqrt{36-x^2}}{4x^2} \, dx
\]
**(A) Which trig substitution is correct for this integral?**
- \( \circ \; x = 36 \sec(\theta) \)
- \( \circ \; x = 6 \sec(\theta) \)
- \( \circ \; x = 6 \sin(\theta) \)
- \( \circ \; x = 36 \sin(\theta) \)
- \( \circ \; x = 36 \tan(\theta) \)
- \( \circ \; x = 6 \tan(\theta) \)
---
**(B) Which integral do you obtain after substituting for \( x \) and simplifying?**
*Note: to enter \( \theta \), type the word theta.*
\[
\int \quad d\theta
\]
---
**(C) What is the value of the above integral in terms of \( \theta \)?**
\[
\boxed{\phantom{text}}
+ C
\]
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