Suppose ?⃗ (?,?)=−??⃗ +??⃗ and ? is the line segment from point ?=(2,0) to ?=(0,3). (a)...

Suppose ?⃗ (?,?)=−??⃗ +??⃗ and ? is the line segment from point ?=(2,0) to ?=(0,3).

(a) Find a vector parametric equation ?⃗ (?) for the line segment ? so that points ? and ? correspond to ?=0 and ?=1, respectively. ?⃗ (?)=

(b) Using the parametrization in part (a), the line integral of ?⃗ along ? is ∫??⃗ ⋅??⃗ =∫???⃗ (?⃗ (?))⋅?⃗ ′(?)??=∫?? ?? with limits of integration ?= and ?=

(c) Evaluate the line integral in part (b).

(d) What is the line integral of ?⃗ around the clockwise-oriented triangle with corners at the origin, ?, and ?? Hint: Sketch the vector field and the triangle.

Expert Solution

Colby Messinger answered 1 year ago

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