1. Suppose a cruise ship docked at a port. Passengers enter and leave the ship through a door located halfway up the ship. At the bottom of the doorframe, there is a square piece of of metal pertruding out from the ship that bridges the gap between the doorframe and the external stairwell located on the dock. Suppose a freak wave caused the ships height to increase in such a way that the square piece of metal rises as the ship rises. Such a rise cause a 10 cm gap between the top of the square piece of metal and the external stairwell. If I placed a metal object in bewteen this gap, would it be crushed under the immense pressure of the ship when the ship returned to it's original height? Or would it actually support the entire ships weight? What if I put my hand under that gap? 2. If I integrate a simple function such as 2x^2. ∫2x^2 dx. The 'dx' imples integrate 2x^2 with respect to x. BUT. Suppose I wanted to integrate an integer such as 5. How would this be written? ∫5. Would there be any dx involved here, or simply ∫5=5x?