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Confused by ConditionalExpression in Integral

Posted 10 years ago

I don't understand why the following gives a ConditionalExpression as a result.

In[124]:= Integrate[Sqrt[u], {u, a^2 Sin[t]^2, a^2}, Assumptions -> { a > 0, Element[t, Reals]}]
Out[124]= ConditionalExpression[-(2/3) a^3 (-1 + Abs[Sin[t]]^3), Tan[t] != 0]

Seems to indicate that t=0 is an invalid value for t? I understand that there is a pole in the complex plane for Sqrt[u], at zero, but t is specified real.

POSTED BY: dave salmon

This is presumably alerting to the fact that the branch cut for the square root function includes the origin.

POSTED BY: David Reiss
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