please help with a mathematical recreational problem I want to compute the area of a right trangle with base 2 and 3, but I want to test the truth of integration of the polar coordinate, so i decide to use this integration formula: $$\int_{0}^{\arctan \frac{3}{2}} \int_0^{\frac{2}{\cos \theta}} r^2 r\;\mathrm{d}r\;\mathrm{d}\theta$$ but with Wolfram Alpha's answer, I get a weird result which differs by 0.06... That make me suspect the truth of the polar coordinate.

Corrected: The area element doesn't have the $r^2$ in it, so the integral should be $\int_{0}^{\arctan \frac{3}{2}} \int_0^{\frac{2}{\cos \theta}} r\;dr\;d\theta$. Alpha says this is $3$.