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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![### Integral Problem Using Trigonometric Substitution
**Problem:**
\[
\int \frac{x^3}{\sqrt{16 + x^2}} \, dx
\]
**Suggested Method:**
- Use trigonometric substitution to solve this integral.
This problem involves an integral of the form \(\frac{x^n}{\sqrt{a^2 + x^2}}\), where trigonometric substitution is often a useful technique. Specifically, consider using the substitution \(x = a \cdot \tan(\theta)\), where \(a = 4\) in this problem, simplifying \(16 + x^2\) into a Pythagorean identity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffedcb44c-84a8-400b-a03e-cc7fbcfb040d%2F09be9119-2812-4f2c-bdd0-f91eab05c749%2Fotiwge8_processed.png&w=3840&q=75)
Transcribed Image Text:### Integral Problem Using Trigonometric Substitution
**Problem:**
\[
\int \frac{x^3}{\sqrt{16 + x^2}} \, dx
\]
**Suggested Method:**
- Use trigonometric substitution to solve this integral.
This problem involves an integral of the form \(\frac{x^n}{\sqrt{a^2 + x^2}}\), where trigonometric substitution is often a useful technique. Specifically, consider using the substitution \(x = a \cdot \tan(\theta)\), where \(a = 4\) in this problem, simplifying \(16 + x^2\) into a Pythagorean identity.
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