Is ∫-1/√(1-x^2) equal to acos(x) and -1*asin(x)?

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The discussion centers on the relationship between the integrals of inverse trigonometric functions, specifically whether ∫-1/√(1-x^2) equals acos(x) and -1*asin(x). It is established that acos(x) is indeed equal to ∫-1/√(1-x^2), while asin(x) equals ∫1/√(1-x^2). The equation arcsin x + arccos x = π/2 is referenced to support the argument. A participant acknowledges a mistake related to the constant of integration, attributing the confusion to exam stress. The conversation highlights the importance of careful consideration in mathematical derivations.
Nikitin
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Since acos(x) = ∫-1/√(1-x^2), and asin(x) = ∫1/√(1-x^2), won't ∫-1/√(1-x^2) = acos(x) = -1*asin(x)?
 
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arcsin x + arccos x = pi/2

so I think what you have is wrong, check again.
 
I doublechecked, but I still can't find my error..
 
Nikitin, is there any chance that you are forgetting the constant of integration?
 
oops, yeh, true :p

sorry, I had a brainfart due to 3 weeks of exams
 

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