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T Find the length of the curve e cos(t) e sin(t) for 0 < t < 2 y (Hint: You can simplify the integrand by expanding the arg
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Aim: to determine the length of the curve. Answer: The equation of curve is given as. 2- e et cost y= et sint where ost <2 Th:. dx et (-sint) + cost.cat dt dx et (cost - sint) ...6) dt similarly Given. y = et sint differentiate with Jespect to t, :Cett cost - 2 cost-sint + sin’t] Cet) } [cost + 2cost. sint + sint bring (ety? as a Common and using the identitiy sin²t + co:::. 12 (et) 2 dt O 2 : - N2 e dt . 2 : । 12 [e (feder) - :. NE- L - V2 (2.18 - 1) . L 2.430 units The length of the curve wi

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