Answer
$$ 6152.69~ \mathrm{N}$$
Work Step by Step
Place the origin at the bottom corner of the plate with the positive $y-$axis pointing upward. The fluid surface
is then at height $y = \pi/2$, and the horizontal strip of the plate at height y is at a depth of $ \pi/2 − y$ and has a width of $\sin y$.
Now, using integration by parts, we find
\begin{aligned}
F &=\rho g \int_{0}^{\pi / 2}\left(\frac{\pi}{2}-y\right) \sin y dy \\
& \text{Integrate by parts:} \\
&=\left.\rho g\left[-\left(\frac{\pi}{2}-y\right) \cos y\right|_{0} ^{\pi / 2}-\int_{0}^{\pi / 2}\cos y\right]\\
&=\left.\rho g\left[-\left(\frac{\pi}{2}-y\right) \cos y-\sin y\right]\right|_{0} ^{\pi / 2}\\
&=\rho g\left(\frac{\pi}{2}-1\right) \\
&=1100 \cdot 9.8\left(\frac{\pi}{2}-1\right)\\
& \approx 6152.69 \mathrm{N}
\end{aligned}
