Suppose C is the curve r( t ) = 〈 t , t 3 〉 , for 0 ≤ t ≤ 2, and F = 〈 x , 2 y 〉 . Evaluate ∫ C F ⋅ T ds using the following steps. a. Convert the line integral ∫ C F ⋅ T ds to an ordinary integral. b. Evaluate the integral in part (a).
Suppose C is the curve r( t ) = 〈 t , t 3 〉 , for 0 ≤ t ≤ 2, and F = 〈 x , 2 y 〉 . Evaluate ∫ C F ⋅ T ds using the following steps. a. Convert the line integral ∫ C F ⋅ T ds to an ordinary integral. b. Evaluate the integral in part (a).
Solution Summary: The author explains how to convert the line integral to an ordinary integral by rewriting F=langle t,2t3rangle .
Suppose C is the curve r(t) =
〈
t
,
t
3
〉
, for 0 ≤ t ≤ 2, and F =
〈
x
,
2
y
〉
. Evaluate
∫
C
F
⋅
T
ds using the following steps.
a. Convert the line integral
∫
C
F
⋅
T
ds to an ordinary integral.
b. Evaluate the integral in part (a).
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.
Evaluate the contour integral z²dz along the following curves.
(a) C₁: the line segment from -i to i.
(b) C₂: the line segment from -i to -1, followed by the line segment from −1 to i.
. Find the slope field of
dy
dx
= 8sinx using GeoGebra.
Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise. A sketch is helpful.
$(4y - 3,2x² + 8). dr. where C is the boundary of the rectangle with vertices (0,0), (6,0). (6,5), and (0,5)
C
$(4y - 3,2x² + 8). dr = (Type an exact answer.)
C
Chapter 17 Solutions
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University Calculus: Early Transcendentals (4th Edition)
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