What is the value of $\frac{d\alpha}{dt} $?

Question

The following question was asked in an exam: Given $\alpha $=$\int_{0}^{\infty}{\frac {dt}{1+t^2}} $. Then is $\frac {d\alpha}{dt} $=$\frac{1}{1+t^2}$? I know that the value $\alpha$=$\frac {\pi}{2} $. So as $\alpha $ is a constant, it's derivative is 0. Am I correct?

Answer 1

I think that the question is silly. But anyway, you are right. And the fact that $\int_0^\infty\frac{\mathrm dt}{1+t^2}=\frac\pi2$ is not important. The only thing that matters is that $\alpha$ is constant.