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In[27]:= Integrate[ DiracDelta[Cos[\[Theta]]] Sin[\[Theta]], {\[Theta], Pi/10, Pi}] Out[27]= 1 and In[37]:= Integrate[ DiracDelta[Cos[\[Theta]]] Sin[\[Theta]], {\[Theta], -Pi/10, +Pi/2}] ...
Thank you for your answer, Neil. You are right, of course. I manage with those vectors operations you refer to, by setting a coordinate system. But I am asking for these type of calculations: ![example][1] that are very usual in physics...