Scotxde = f COS X sin x -dx

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.
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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