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Determine the area bounded by the curve xt t2 2t y t

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Unformatted text preview: /dt)2 + (dy/dt)2 dt = 0 0 (et + e−t ) dt = et − e−t 4 0 = e4 − e−4 5. Determine the area bounded by the curve x(t) = t2 + 2t, y (t) = sin (t) on 0 ≤ t ≤ π . 1.0 0.5 0.0 5 0 π 10 15 π y dx = 0 sin (t)(2t + 2) dt 0 = (−2t cos (t) + 2 sin (t) − 2 cos (t))π = 2π + 4. 0 6. Convert the given points or fuctions from polar to rectangular (Cartesian). √ 2π 333 (a) (2, π ) = (−2, 0) 3, = −, 3 22 (b) 4, − √ = (2 3, −2) π 6 −2, 3π 4 √ √ = ( 2, − 2) (c) r = 4 x2 + y 2 = 16 (d) r = 3 cos (θ) + 3 sin (θ) (multiply both sides by r ) x − 3...
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