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darkmagic
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Homework Statement
How can I integrate this:
\int sin (nt) sin (n \pi t) dt
This actually in the Fourier series.
Integral of trigonometric functions
- Thread starter darkmagic
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SUMMARY
The integral of the product of sine functions, specifically \(\int \sin(nt) \sin(n \pi t) dt\), can be solved using the trigonometric identity \(\sin a \sin b = \frac{\cos(a-b) - \cos(a+b)}{2}\). This identity simplifies the integration process by transforming the product of sine functions into a difference of cosine functions. The application of this identity is crucial for solving integrals in Fourier series analysis.
PREREQUISITES- Understanding of trigonometric identities, specifically sine and cosine functions.
- Familiarity with integral calculus and techniques for solving definite and indefinite integrals.
- Knowledge of Fourier series and their applications in signal processing.
- Basic skills in mathematical notation and manipulation of algebraic expressions.
- Study the derivation and applications of the trigonometric identity \(\sin a \sin b = \frac{\cos(a-b) - \cos(a+b)}{2}\).
- Learn techniques for integrating products of trigonometric functions using identities.
- Explore the fundamentals of Fourier series and their role in analyzing periodic functions.
- Practice solving integrals involving sine and cosine functions in various contexts.
Students and professionals in mathematics, physics, and engineering who are working with Fourier series, trigonometric integrals, or signal analysis will benefit from this discussion.
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