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Very short integration giving me wrong results, I am missing something?

Guillermo Sanchez
Posted 10 years ago

This integral ?(cos^2(x)*cot(x))dx is not calculating right, I have tried two other websites and they do give me like I did in my notebook, but in this website its throwing log(sin(x)) + (cos^2(x))/2 instead of log(sin(x)) - (sin^2(x))/2, can you please look into it and tell me what is happening, I'm relying a lot on this website and have bought the Pro version, I have also tried giving any value for "x" on both answers and they have different results, thanks!
POSTED BY: Guillermo Sanchez
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David Keith
David Keith
Posted 10 years ago

The integration constant can be any constant. For a definite integral it is determined by the boundary condition or initial value. But if g(x) is an antiderivative of f(x), then so is g(x) + c, with c being independent of x, since then dc(x)/dx = 0. And your quite welcome, Guillermo. Calculus is a lot of fun.
POSTED BY: David Keith
David Keith
David Keith
Posted 10 years ago

Take log(sin(x)) + (cos^2(x))/2 and substitute cos^2(x) = 1-sin^2(x) and you get log(sin(x)) - (sin^2(x))/2 + 1/2

The 1/2 disappears when you differentiate, so both are correct. Another way to look at it is the indefinite integral comes with an integration constant, which can consume the 1/2.
POSTED BY: David Keith

That makes sense!! So the integration constant that always comes after integrating, in this case would be the 1/2? I never would have thought of that haha, I definitely need a lot more practice if I want to pass Calculus :D

Thanks for the reply!
POSTED BY: Guillermo Sanchez
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