Consider the line integral / F. dr, where C is given by the vector function r(t). F(x, y, z) = sin(x)i + cos(y)j + xzk r(t) = t5i - t³j + tk, 0sts 1 Find the following functions. F(r(t)) = r'(t) = F(r(t)) · r'(t) = Evaluate the line integral.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 20T
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Consider the line integral /
F- dr, where C is given by the vector function r(t).
F(x, y, z) = sin(x)i + cos(y)j + xzk
r(t) = ti – t³j + tk, 0<t< 1
Find the following functions.
F(r(t)) =
r'(t) =
F(r(t)) · r'(t) =
Evaluate the line integral.
Transcribed Image Text:Consider the line integral / F- dr, where C is given by the vector function r(t). F(x, y, z) = sin(x)i + cos(y)j + xzk r(t) = ti – t³j + tk, 0<t< 1 Find the following functions. F(r(t)) = r'(t) = F(r(t)) · r'(t) = Evaluate the line integral.
Consider F and C below.
F(x, y) = x² i + y² j
C is the arc of the parabola y = 4x² from (-1, 4) to (0, 0)
(a) Find a function f such that F = vf.
f(x, y) =
(b) Use part (a) to evaluate /
Vf - dr along the given curve C.
Transcribed Image Text:Consider F and C below. F(x, y) = x² i + y² j C is the arc of the parabola y = 4x² from (-1, 4) to (0, 0) (a) Find a function f such that F = vf. f(x, y) = (b) Use part (a) to evaluate / Vf - dr along the given curve C.
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