Engineering Calculus Notes 222

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

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210 CHAPTER 2. CURVES (a) y = x n , 0 x 1 (b) y = e x , 0 x 1 (c) y = ln x, 1 x e (d) y = sin x, 0 x π (e) braceleftbigg x = a cos θ y = b sin θ , 0 θ 2 π (f) braceleftbigg x = e t + e t y = e t e t , 1 t 1 2. Find the length of each curve below. (a) y = x 3 / 2 , 0 x 1 (b) y = x 2 / 3 , 0 x 1 (c) y = x 3 3 + 1 4 x , 1 x 2 (d) y = integraldisplay x 1 radicalbig t 4 1 dt, 1 x 2 (e) braceleftbigg x = sin 3 t y = cos 3 t , 0 t π 4 (f) x = 9 t 2 y = 4 t 3 z = t 4 , 0 t 1 (g) x = 8 t 3 y = 15 t 4 z = 15 t 5 , 0 t 1 (h) x = t 2 y = ln t z = 2 t , 1 t 2 (i) braceleftbigg x = sin θ y = θ + cos
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