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I learned some tricks in my Calculus lecture that I am thinking, "How the fuck is that even considered a valid proof?"
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Well, it dealt with the integral of cos^2x, since we were learning to use trig identities to solve integrals.(at least, I think that was the integral. I would have to check my notes again). The way it was proven was through taking the integral, and since another integral popped up, we solved for that integral, which would lead to the same integral that we were solving originally. We would then subtract that integral about the original one and it was solved.