For part a, it is asking me to take a line integral of a vector field (i.e. evaluate the integral using a line integral). B. Attached is the fundamental theorem for line integrals for reference. THEOREM 17.4 Fundamental Theorem for Line IntegralsLet R be a region in R? or R' and let o be a differentiable potential function definedon R. If F = V¢ (which means that F is conservative), thenF•T ds =F.dr = q(B) – q(A),CCfor all points A and B in R and all piecewise-smooth oriented curves C in R from Ato B. 1. Let F(x, y, z) = (y² + 2z, 2xy + 4, 2x), and let the curve C be described by r = t, y=t², z= t³for 1

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Answered: Let F(x, y, z) = (y² + 2z, 2xy + 4,…

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Let F(x, y, z) = (y² + 2z, 2xy + 4, 2x), and let the curve C be described by x = for 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 33E

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Question

For part a, it is asking me to take a line integral of a vector field (i.e. evaluate the integral using a line integral). B. Attached is the fundamental theorem for line integrals for reference.

THEOREM 17.4 Fundamental Theorem for Line Integrals
Let R be a region in R? or R' and let o be a differentiable potential function defined
on R. If F = V¢ (which means that F is conservative), then
F•T ds =
F.dr = q(B) – q(A),
C
C
for all points A and B in R and all piecewise-smooth oriented curves C in R from A
to B.

1. Let F(x, y, z) = (y² + 2z, 2xy + 4, 2x), and let the curve C be described by r = t, y=t², z= t³
for 1<t < 2.
a) Evaluate
F.T ds using the approach from text section 17.2.
b) Evaluate
F.T ds using the Fundamental Theorem for Line Integrals from text section 17.3.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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