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DQ
Numerade Educator

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Problem 6 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int (x - 1) \sin \pi x dx $

Answer

$\int(x-1) \cdot \sin (\pi x) d x=\frac{1-x}{\pi} \cdot \cos (\pi x)+\frac{1}{\pi^{2}} \sin (\pi x)+C$

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Video Transcript

Oh, hello. So today we're evaluating them to go of experts. One time sign of pi X, the X There really should be a parentheses around the pie ex together because you want to take a sign of pious IX. This is a standard, Ah, integration by parts problems. So you want to find you in a DVD to decompose it into, um I want to find a you that basically disappears after immigrating after differentiating once or twice, or however many times this case, he only wanted differentiate ones. You equals X minus one in this case, and Devi is equal to sign of pi X t x which is you're able to integrate basically so differentiating you, you got d equals DX integrating Devi you get vehicles native one over pi co sign of pi X. Put it all together you get native one of her pi X minus one co sign of pi X minus negative one reply. Integral of coastline of pi X, The X I like to put all my constance outside of the interval because it's easier to work on afterwards. Ah, simplifying you get native one of reply expense one co sign a pi X plus one over pi times one of reply again because you get no another integration from the coastline up Iraq's plus C musical to native wanna rip I express one cosign a pi x plus one over pi squared sine of pi x plus e.