MATH 115 Final: MATH 115 UPenn 115FinalAns2012A Exams
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February 22, 2007: (18 points) evaluate the following integrals: (a) z x3 sin(x4 + 7) dx. Solution: let u = x4 + 7, then du = 4x3 dx and. [ cos(u)] + c = cos(x4 + 7) + c (b) z e3 e x dx. If x = e then u = ln(e) = 1, and if x = e3 then. Solution: let u = ln x, then du = 1 u = ln(e3) = 3 and. 3 (c) z x5 4 x3 + 2 dx. Solution: let u = x3 + 2, then du = 3x2 dx and x3 = u 2. Z x5 4 x3 + 2 dx = z x3 (x3 + 2)1/4 x2 dx = 1: (18 points) evaluate the following integrals: (a) z x ex dx. Solution: use integration by parts and let u = x and dv = ex dx, then du = dx and v = ex and.
