- #1
darkmagic
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Homework Statement
How can I integrate this:
[tex]\int sin (nt) sin (n \pi t) dt [/tex]
This actually in the Fourier series.
The general formula for finding the integral of a trigonometric function is ∫sin(x)dx = -cos(x) + C or ∫cos(x)dx = sin(x) + C, where C is the constant of integration.
To integrate trigonometric functions with powers, use the power reduction formulas: sin^n(x) = (1-cos^2(x))^(n/2) and cos^n(x) = (1+cos^2(x))^(n/2). Then use substitution and integration by parts methods to solve the integral.
Yes, trigonometric identities such as the double angle formulas, half angle formulas, and sum and difference formulas can be used to simplify and solve integrals of trigonometric functions.
Yes, when integrating trigonometric functions, special cases such as odd or even powers, the presence of a square root, or the presence of a constant may require the use of specific techniques such as substitution or trigonometric identities.
The process for evaluating definite integrals of trigonometric functions involves finding the antiderivative of the function, substituting the upper and lower limits of integration, and then subtracting the values to find the final answer.