Find the line integrals of F = 2yi + 3xj + zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path C₁: r(t) = ti + tj + tk, 0≤t≤ 1 b. The curved path C₂: r(t) = ti +t²j+t4k, 0≤t≤1 c. The path C3 UC4 consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Just need part c for both questions. The answers I have are incorrect. 

Find the line integrals of F = 2yi + 3xj + zk
from (0,0,0) to (1,1,1) over each of the
following paths.
a. The straight-line path C₁:
r(t) = ti + tj + tk, 0 ≤t≤ 1
b. The curved path C₂: r(t) = ti + t²j + tªk,
0≤t≤1
c. The path C3 UC4 consisting of the line
segment from (0,0,0) to (1,1,0) followed by
the segment from (1,1,0) to (1,1,1)
(0, 0, 0)
C₁ (1, 1, 1)
CA
(1, 1, 0)
a. The line integral of F over
the straight-line path C₁ is 3
(Type an integer or a
simplified fraction.)
b. The line integral of F over the
19
6
(Type an integer or a
simplified fraction.)
curved path C₂ is
c. The line integral of F over the
47
6
(Type an integer or a
simplified fraction.)
path C3 UC4 is
Transcribed Image Text:Find the line integrals of F = 2yi + 3xj + zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path C₁: r(t) = ti + tj + tk, 0 ≤t≤ 1 b. The curved path C₂: r(t) = ti + t²j + tªk, 0≤t≤1 c. The path C3 UC4 consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0, 0, 0) C₁ (1, 1, 1) CA (1, 1, 0) a. The line integral of F over the straight-line path C₁ is 3 (Type an integer or a simplified fraction.) b. The line integral of F over the 19 6 (Type an integer or a simplified fraction.) curved path C₂ is c. The line integral of F over the 47 6 (Type an integer or a simplified fraction.) path C3 UC4 is
Find the line integral of F = 4√√zi - 2xj+√yk,
from (0,0,0) to (1,1,1) over each of the following
paths.
a. The straight-line path C₁ : r(t) = ti + tj + tk,
0≤t≤1
b. The curved path C₂: r(t) = ti + t²j + tªk, 0≤t≤1
c. The path C3 UC4 consisting of the line
segment from (0,0,0) to (1,1,0) followed by the
segment from (1,1,0) to (1,1,1)
...
7
a. The line integral of F over the straight-line path C₁ is
3
(Type an integer or a simplified fraction.)
4
b. The line integral of F over the curved path C₂ is
(Type an integer or a simplified fraction.)
(0, 0, 0)
47
c. The line integral of F over the path C3UC4 is
15
(Type an integer or a simplified fraction.)
C₁
C3
(1, 1, 1)
CA
(1, 1, 0)
Transcribed Image Text:Find the line integral of F = 4√√zi - 2xj+√yk, from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path C₁ : r(t) = ti + tj + tk, 0≤t≤1 b. The curved path C₂: r(t) = ti + t²j + tªk, 0≤t≤1 c. The path C3 UC4 consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) ... 7 a. The line integral of F over the straight-line path C₁ is 3 (Type an integer or a simplified fraction.) 4 b. The line integral of F over the curved path C₂ is (Type an integer or a simplified fraction.) (0, 0, 0) 47 c. The line integral of F over the path C3UC4 is 15 (Type an integer or a simplified fraction.) C₁ C3 (1, 1, 1) CA (1, 1, 0)
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