MATH 126 Study Guide - Midterm Guide: Conditional Convergence, Hyperbolic Function
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Express the volume as an integral and evaluate it: evaluate the integral z, consider the integral z . 1 the value of the integral. dx. (x 1)(x2 + x + 1) (1/2) x + (2/3) 3 x. If so, nd: the curve y = cosh x, 1 x 1, is rotated about the x-axis. Find the area of the resulting surface: (a) express the area as an integral. (b) evaluate the integral for the area. Express the nal answer in terms of a hyperbolic function: the end of an open tank containing water is vertical and is a semicircle with diameter 16 meters at the top. The surface of the water is 4 meters from the top. Set up an integral for the hydrostatic force exerted against the end of the tank. Clearly state any test you use and show that all of the necessary conditions for applying the test are satis ed. (a) (b)
