I hope you are having a great day, I am learning integral calculus and our teacher left us an interesting problem, however, I don't really understand how to pose the integrals he asked me for.
The question:
The figure shown below represents the cross section of a submersible and some of its dimensions. The green region is a parabolic segment that cuts the $x$-axis at point $A = (-\sqrt{20}, 0)$ and has a vertex at point $B = (0,-2)$. The red region is a semicircle of radius $1$ and centered at $(3, -1)$. Based on this scheme, propose the integral that computes the hydrostatic force on the cross section of the submersible, when it is at 500m, 1000m, 1500m, 2000m, and 2500m, respectively.
So I know that we can define the integral as: $F = \int_a^b \rho g h(x) \, dA$.
But, in this case, we need both functions, how can I get to that integral.
Thank you, and have a great day.
