MATH 0120 Quiz: Math 0120 Quiz 5(0120) Solutions spring 2013-312
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S o l u t i o n s: [5 points] evaluate the integral. Substitution: u = ln x, du = 1. 4 dx, ln 1 = 0, ln e = 1. = 1 0 = 1: [5 points] evaluate the integral. By parts: u = ln x, du = 1 x dx, dv = 4x3 dx, v = x4. 1 x dx = e4 ln e 14 ln 1 e. 4 (cid:12)(cid:12)(cid:12)(cid:12) bonus problem [5 points extra] find the area of the region enclosed by the graph of the function f (x) = 1 x2, the x-axis, the line x = 0, and the line x = 2. The rst one is below the graph of f (x) and. Solution: above the x-axis when x is between 0 and 1 since f (x) = 0 when x = 1. The second part lies below the x-axis and above the graph of f (x).
