Consider the textbook example problem $2\mathrm{.}6,$ as shown in figure $1.$ This time, instead of using formulas, perform a surface integral over the disk to determine the magnitude and location of the resultant force exerted on the gate by the water. This can be understood as summing over the infinitesimal pressure force and resultant moment on a small sectorial area $dA=rddr($see inserted figure$)$ over the surface of the circular gate.

Hint: Recall that you have conducted a similar surface integral in homework assignment $1.$ There are also many contents in lecture slides so you don't need to start from scratch. $(3$ pts$)$

Figure $1$: Textbook Example $2\mathrm{.}6$: hydrostatic force on a plane circular surface.