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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![### Integration of Trigonometric Functions
**Integrating the Cotangent Function:**
\[ \int \cot x \, dx = \int \frac{\cos x}{\sin x} \, dx \]
This integral expresses the cotangent function in terms of its equivalent using cosine and sine functions. By rewriting cotangent \((\cot x)\) as \(\frac{\cos x}{\sin x}\), the integral becomes simpler to solve by recognizing it as a form suitable for substitution.
**Integrating the Tangent Function:**
\[ \int \tan x \, dx = \int \frac{\sin x}{\cos x} \, dx \]
Similarly, this integral expresses the tangent function in terms of sine and cosine functions. By rewriting tangent \((\tan x)\) as \(\frac{\sin x}{\cos x}\), it can also be solved more easily using standard integration techniques.
These equations are fundamental in calculus and are often used in more advanced mathematical problems involving trigonometric integrals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4dca08d-d7c1-4511-81d7-e3b17171b463%2Faf2deefc-b788-4cb4-9e1b-8dadc33984c2%2F9jokied_processed.png&w=3840&q=75)
Transcribed Image Text:### Integration of Trigonometric Functions
**Integrating the Cotangent Function:**
\[ \int \cot x \, dx = \int \frac{\cos x}{\sin x} \, dx \]
This integral expresses the cotangent function in terms of its equivalent using cosine and sine functions. By rewriting cotangent \((\cot x)\) as \(\frac{\cos x}{\sin x}\), the integral becomes simpler to solve by recognizing it as a form suitable for substitution.
**Integrating the Tangent Function:**
\[ \int \tan x \, dx = \int \frac{\sin x}{\cos x} \, dx \]
Similarly, this integral expresses the tangent function in terms of sine and cosine functions. By rewriting tangent \((\tan x)\) as \(\frac{\sin x}{\cos x}\), it can also be solved more easily using standard integration techniques.
These equations are fundamental in calculus and are often used in more advanced mathematical problems involving trigonometric integrals.
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