Greetings everyone! I am new to this forum. I take a variety of mathematic courses and needed some help so found this website. Its great to see a variety of people interested in mathematics! In my current calculus class, we are learning about Integral areas in geometric shapes and application in physics. Here are a few problems practice problems that I had trouble with. If anyone can solve them (you can put the last definite integral formula to be solved) with an explanation, I'd appreciate that! 1.) A dam is approximatly shaped like a trapezoid with height 726 feet, width at top of 1244 ft and width at base of 660 ft. Determine total force on dam if the water is 700ft deep. (Water weighs about 62.4 lb/feet cubed.) 2.) A rectangular pool measures 10 feet deep, 15 feet wide, and 40 feet long. It is filled with pure water to 6 inches below the top. If a one horsepower motor can perform 550 ft*lbs of work per second, then what size motor is required to empty the pool in 1 hour? The weight density of pure water is about 62.4 lbs per cubic feet. 3.) Soot produced by a garbage incinerator spread out in a circular pattern. The depth, H(r) (in mm) of the soot deposited each month at a distance r kilometers from the incinerator is gvien by H(r)= 0.23e^-2r. Determine the volume of soot in meters cubed, deposited within a 5km radius of the incinerator. 4.) Cables connecting the towers of the George Washignton Bridge are approximated by the parabola: y=0.00013x^2 ft, where x is the horizontal distance from the vertex of the cable. If the distance between the two towers is 3500 feet, then determine the exact length of the cable that spans them. Also give the 4 sign. fig approximation.