MATH101 Study Guide - Midterm Guide: Volume Integral, Scilab, Partial Fraction Decomposition
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MATH101 Full Course Notes
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Solutions for math 101 february 2009 midterm: part (a). We use the method of cylindrical shells to set up the volume integral. The region bounded by y = x (cid:0) x2 and y = 0 looks like. The line x = 2 is to the right of the region. Therefore, the (cid:147)radius(cid:148)is 2(cid:0)x, the (cid:147)circumference(cid:148)is 2(cid:25) (2 (cid:0) x) and the (cid:147)height(cid:148)is x(cid:0)x2. The region bounded by the curves y = cos (x), y = 1 (cid:0) cos (x), x = 0 and x = (cid:25) looks like. 21. 510. 500. 40. 30. 20. 10xyxy32. 521. 510. 5021. 510. 50(cid:173)0. 5(cid:173)1xyxythe curves intersect when cos (x) = 1 (cid:0) cos (x) =) cos (x) = 0 jcos (x) (cid:0) [1 (cid:0) cos (x)]j dx =z (cid:25) 2 cos (x) (cid:0) 1 dx +z (cid:25) 0 + [x (cid:0) 2 sin (x)](cid:25) (cid:25)=3. = 2 sin ((cid:25)=3) (cid:0) (cid:25)=3 + (cid:25) (cid:0) [(cid:25)=3 (cid:0) 2 sin ((cid:25)=3)] Let u = x and dv = sin ((cid:25)x) dx.