I have to solve the following equation using Mathematica.
$\frac{8 \pi \sqrt{a^2+b^2}\ e^{-a \pi^2}}{b}(b\ \cos b\ \pi^2+a\ \sin b \ \pi^2)\int\limits_0^1 e^{-a\ \pi^2 u^2}\cos b\ \pi^2 u^2 ~du=1$.
For each $ \frac{1}{2}\le a \le 2$, there exists many $b$'s satisfying the equation. I want to find the first or minimum value of $b$ satisfying the above equation. I tried NSolve
but it is not working. I tried FindRoot
, it's working but I need to guess the root. Since I need many points to make list plot so it is very hard.