MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 12.8 Solutions Fa 2014

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

November 17, 2015: find the length of the curve: r(t) = h2 + 3t, 1 5t, 4 3ti, on [1, 6]. Solution: since r (t) = h3, 5, 3i, the arc length of our curve is given by. 1: find the length of the curve: r(t) = h2et sin(t), 2et, 2et cos(t)i, on [0, ln(3)]. Solution: let f (t) = 2et sin(t), g(t) = 2et, h(t) = 2et cos(t). Then f (t) = 2et(sin(t) + cos(t)) g (t) = 2et h (t) = 2et( sin(t) + cos(t)). Then f (t)2 = 4e2t(sin2(t) + 2 sin(t) cos(t) + cos2(t)) g (t)2 = 4e2t h (t)2 = 4e2t(sin2(t) 2 sin(t) cos(t) + cos2(t)). = 4e2t(sin2(t) + 2 sin(t) cos(t) + cos2(t) + 1. + sin2(t) 2 sin(t) cos(t) + cos2(t)) = 4e2t(2 sin2(t) + 2 cos2(t) + 1) 0 p(3 + 3 cos )2 + ( 3 sin )2dt. 0 q9 + 18 cos + 9 cos2 + 9 sin2 )dt.