MAT 127 Midterm: S16mt1sol
31 Jan 2019
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February 19, 2016: (16 pts) a gorge has the shape of the parabola y = x2, with distances measured in feet. A dam is to be constructed, with water level 100 ft. find the hydrostatic force on the dam. The width at height y is w (y) = 2x = 2y1/2. The depth of water at height y is 100 y. 5 105] lbs: (16 pts) the region below the graph y = 1 x2 and above the x-axis is rotated around the line x = 1. Based on the shape of the region, it is much easier to use dx in this problem. This choice of variable leads to cylindrical shells: Here r = (dist. from x to axis of rotation) = (1 x) and h = 1 x2. 1 (1 x2 x + x3)dx. Noting that x and x3 are odd functions and we integrate over a symmetric interval, these terms contribute 0 to the integral.
