Math 1B Section 112 Quiz 5 Thursday 27 September 2007 Theo Johnson Freyd theojf math berkeley edu Name 1 3 pts Find the length of the curve y ln cos x as x ranges between 0 and 4 R 4 p 1 y 0 2 dx 0 R 4 p 0 1 sin x cos x 2 dx R 4 0 sec x dx length of curve 4 ln sec x tan x 0 ln 2 2 1 ln 1 ln 1 2 5 pt 5 pt 1 pt 5 pt 5 pt 2 3 pts Find the area of the surface of revolution generated by rotating the curve y x3 as x ranges between 1 and 3 around the x axis R3 p 0 2 1 y 1 y dx R3 2 x 1 x3 1 9x4 dx R 1 9 34 du 2 u 10 u 36 area of surface 2 270 10 2 18 3 3 2 27 730 u3 2 1 103 2 5 pt 5 pt 1 pt 1 pt 3 4 pts Find the area of the surface of revolution generated by rotating the curve ex e x y cosh x as x ranges between 0 and 2 around the y axis 2 R2 p 0 2 0 x 1 y dx r R2 x x 2 dx 2 0 x 1 e e 2 area of surface 2 5 pt 5 pt R 2 q 2 e2x 1 e 2x dx 4 0 x R 2 x x 2 0 x e e dx 2 R2 R2 0 xex dx 0 xe x dx 2 1 pt 2 xex ex 20 xe x e x 0 1 5 pt e2 1 3e 2 1 2 e2 3 e2 5 pt 2
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