Question

Please show work on the first problem.

Corresponding Worksheet: Line Integrals All books, notes, and electronic devices should be put away during this quiz. 1. Let C be a curve in the ry-plane parameterized by Ft), a stab. What is the significance/meaning of the integral 1 ds? 2. Which the following represents the line integral of f(x,y) - 2x + y along the curve given by (21. + 3) where 0 <t<1. Circle your answer. t) - S (56 +3)/34 + 6 + ode ['15e + 3)V5 de I (6 + 6 + ®) V6€ + 6 +94 [(+6e + 9) Vode ('6e + 3) dt 4 5 6 7 8 9

Answer 1

1. C is parameterized by r(t); astsb. The integral ſids = | ||:"(t)||dt which represents the length of the curve r(t) in the interval astsb. 2. f(x, y) = 2x +y, r(t) = (2,t+3) =r'(t)=(2,1)= || (1)|| = V22 +1° = v5 and f(r(t))=4t+t+3= 51 +3 : The line integral is (51 +3) F5d