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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≤ 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.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.)
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 (...)
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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