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Problem 72 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^{T/2}_0 \sin (2\pi t/T - \alpha) \, dt $

Answer

$\frac{T}{\pi} \cos \alpha$

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Video Transcript

say that are you is what's in parentheses. This means that our DT would be capital t over to pie, do you? Which means we now have the integral of as you can see from the substitution we did earlier. The lower case t goes away using the power will we know we can now integrate. Obviously negative night, it becomes positive. This is because we have negative co sign you times the constant as are integral. So we end up with negative negative which, as I said, it's positive. Which gives us t over pi times co sign Hey!