Question

. Find the mass of a thin wire lying on the curve r(t) = (2t, e', t), 0 <t<l with density 8 = V5+e". (Note: You may need to use the fact that (e) = e.) 1 4+ -e?

Answer is in blue please show how to get to the answer.

Answer 1

on the curve with Qura- to find the mass of a thin wire dying Lt)<2t, et t> osts 1 denasty. S = 5tex Pelutions Curve C is parameterzed by X(t) = at y(t) = et z(t) = t fostaty Now, We compuk luct)l; 4 id z(1) dt () = apo J + (aq) 1601 felles fe familie (2)² + [et² + 117 4+ e + +1 f: (e+9=) 1v1). Istet Now density S= 5tex Il est 71= 21. t S = Jste 2t برکنا ky the defination of line integral 56442) as S. Tritat ܛܘ

Ister ( Isten dt. (5tet) at st dt t fon eet dt 5140. + Leat) 2 511-07+ le? - 1 1 2 5* le² 1 2 2 4.5+ le? 2 Jutal muss the wire id M(0) = 4.5t I e? 2 - Hence, the answer is the correct answer, as the & dution i¢ done astep by step with proper Checking and an accuracy