Engineering Calculus Notes 222

Engineering Calculus Notes 222 - 210 CHAPTER 2. CURVES (a)...

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Unformatted text preview: 210 CHAPTER 2. CURVES (a) y = xn , y = ex , 0≤x≤1 0≤x≤1 (b) (c) y = ln x, 1 ≤ x ≤ e y = sin x, 0 ≤ x ≤ π (e) x = a cos θ , y = b sin θ (f) x = et + e−t , y = et − e−t (d) 0 ≤ θ ≤ 2π −1 ≤ t ≤ 1 2. Find the length of each curve below. (a) y = x3/2 , 0 ≤ x ≤ 1 y = x2/3 , 0 ≤ x ≤ 1 x3 1 (c) y = + , 1≤x≤2 3 x 4x t4 − 1 dt, 1 ≤ x ≤ 2 y= (b) (d) 1 (e) x = sin3 t , y = cos3 t x (f) y z x y (g) z x (h) y z (i) = 9t2 = 4t3 , = t4 0≤t≤ 0≤t≤1 = 8t3 = 15t4 , = 15t5 = t2 = ln t , = 2t 0≤t≤1 1≤t≤2 x = sin θ , y = θ + cos θ 3t x = (j) y = 4t sin t , z = 4t cos t 3. Calculate C π 4 0≤θ≤ 0≤t≤ π 2 5 4 f ds: (a) f (x, y ) = 36x3 , C is y = x3 from (0, 0) to (1, 1). (b) f (x, y ) = 32x5 , C is y = x4 from (0, 0) to (1, 1). ...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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