A vertical plate is submerged (or partially submerged) in water and has the indicated shape. Explain how to approximate the hydrostatic force against one side of the plate by a Riemann sum.Then express the force as an integral and evaluate it.
$$(y-4 x-1)^{2} d x-d y=0$$
$$(t+x+2) d x+(3 t-x-6) d t=0$$
$$\left(y e^{-2 x}+y^{3}\right) d x-e^{-2 x} d y=0$$
$$8 .\left(y^{3}-\theta y^{2}\right) d \theta+2 \theta^{2} y d y=0$$
In Problems $1-6,$ identify the equation as separable, linear, exact, or having an integrating factor that is a function of either $x$ alone or $y$ alone.$$\left(2 y^{3}+2 y^{2}\right) d x+\left(3 y^{2} x+2 x y\right) d y=0$$
