Question

evaluate the double integral

Answer 1

\[\int\limits_{0}^{\frac{ \pi }{ 4 }}\int\limits_{1}^{2} r \tan^{-1} (\tan \theta)dr d \theta \]

Answer 2

You're only integrating with respect to r for the first portion there. So tan-1(tan theta) is just a constant

Answer 3

\[\int\limits_{0}^{\pi/4} \tan^{-1} (\tan \theta) d \theta *\int\limits_{1}^{2}r dr\]

Answer 4

I did'nt get the d(theta)

Answer 5

Once you're there, if you have issues integrating the trig function, I'd just wolfram alpha it. I still use their integral calculators.

Answer 6

http://integrals.wolfram.com/index.jsp?expr=tan%5E-1%28tanx%29&random=false