Hydrostatic force with calculus

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That is my problem. I attempt to solve it by setting up an x-y axis with the origin at the center of the semicircle.

I then set up the following:

Hydrostatic Force =

INTEGRAL of: (width of a given strip)(height of a given strip)(density of water)(force gravity)(distance under water a given strip is)

Which with numbers looks like this:

INTEGRAL of: (sqrt(4-y^2))(dy)(1000)(9.8)(10-y)

I used trig substitution for the sqrt(4-y^2) and it simplifies to cos/cos, and go onto solve the integral with the bounds of 0-2. What am i doing wrong?