Math video, solving integral ln(a*sin(x))

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Re: Math video, solving integral ln(a*sin(x))

That's weird. He starts by saying that he has already proved, I presume in a previous post, that $$\int_0^\pi ln(sin(x))dx= -2\pi$$. Then he integrates $$\int_0^\pi ln(a sin(x))dx$$ by differentiating with respect to a to get a simpler integral where the constant can be related to $$\int_0^x ln(sin(x))dx$$.

I think it would be simpler to use the fact that $$ln(a sin(x))= ln(a)+ ln(sin(x))$$. So the integral of ln(a sin(x)) is the integral of ln(a), a constant, which is $$ln(a)\pi$$ plus the integral of ln(sin(x) which was already known.

HallsofIvy

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Re: Math video, solving integral ln(a*sin(x))

I proved it in another video, yes. I havent solved any problem using differentiation, so i thought using it here, to show it off, would be a nice idea.
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