Find the work done by F over the curve in the direction of increasing t. F = 2zi + 2xj + 2yk, r(t) = (sin t)i + (cost)j + tk, 0≤t≤ 2π The amount of work done is (Type an exact answer, using as needed.)
Find the work done by F over the curve in the direction of increasing t. F = 2zi + 2xj + 2yk, r(t) = (sin t)i + (cost)j + tk, 0≤t≤ 2π The amount of work done is (Type an exact answer, using as needed.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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![Find the work done by F over the curve in the direction of increasing t.
F = 2zi + 2xj + 2yk, r(t) = (sin t)i + (cost)j + tk, 0≤t≤2
The amount of work done is
(Type an exact answer, using as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50406375-c106-4290-890a-56c43ddee553%2F1c9d9a52-e36e-4af1-a41c-cdc12c181757%2Fulu4xza_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the work done by F over the curve in the direction of increasing t.
F = 2zi + 2xj + 2yk, r(t) = (sin t)i + (cost)j + tk, 0≤t≤2
The amount of work done is
(Type an exact answer, using as needed.)
![Find the circulation and flux of the field F = -5yi +5xj around and across the closed semicircular path that consists of the semicircular arch
r₁ (t) = (pcos t)i + (psin t)j, 0≤t≤, followed by the line segment r₂(t)=ti, -pstsp.
The circulation is (Type an exact answer, using as needed.)
(Type an exact answer, using as needed.)
The flux is
(...)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50406375-c106-4290-890a-56c43ddee553%2F1c9d9a52-e36e-4af1-a41c-cdc12c181757%2Fcwiq8dnu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the circulation and flux of the field F = -5yi +5xj around and across the closed semicircular path that consists of the semicircular arch
r₁ (t) = (pcos t)i + (psin t)j, 0≤t≤, followed by the line segment r₂(t)=ti, -pstsp.
The circulation is (Type an exact answer, using as needed.)
(Type an exact answer, using as needed.)
The flux is
(...)
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