integrate fails in a sign when working with trigonometric functions under the root

[rtoy]

Imported from SourceForge on 2024-07-09 11:14:10 Created by dikiy84 on 2023-10-26 10:52:23 Original: https://sourceforge.net/p/maxima/bugs/4201

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 integrate(sqrt(1-sin(t)^2)*cos(t), t, %pi, %pi/2);

should give %pi/4, but gives -%pi/4. I think the problem is, then in the integration domain sqrt(1-sin²t) = |cos t| = -cos t.

But maxima for some reason works with |cos t| = cos t

[rtoy]

Imported from SourceForge on 2024-07-09 11:14:12 Created by dikiy84 on 2023-10-26 16:10:32 Original: https://sourceforge.net/p/maxima/bugs/4201/#b6d2

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The same problem appears if we change it to:

integrate(sqrt(1-sin(t)^2)*cos(t), t, %pi/2, %pi);

is should give -%pi/4, but returns %pi/4

Maxima 5.43.2

[rtoy]

Imported from SourceForge on 2024-07-09 11:14:15 Created by robert_dodier on 2023-10-30 05:22:59 Original: https://sourceforge.net/p/maxima/bugs/4201/#5dd5

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• labels: --> integrate, defint, sqrt, trigonometry