I may need some help with the following problem.

We have

$$
y(\omega)=a+\omega\cdot b - \frac{1}{2}\cdot\omega^2\cdot g
$$
where $g$ is the gravity vector $g=\binom{0}{\lambda}$, $\lambda \approx 9,81\frac{m}{s^2}$, $a=\binom{0}{0}$ and $b=\dot y(0)=\binom{b\_1}{b\_2}$ with $b\_1 \neq 0$.

 The starting velocity $|\dot y(0)| $ is given.

 The question is : Under which angle a projectile has to be launched to maximize the area under the parabolic path.

My Idea was to integrate $y$. Find the maximum by differetiating it (which would mean solving $y(\omega)=0$). And solving that for $b\_1$. Is this correct?