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Let F = Vf and f = 4x²y - 5z. Calculate F. dr for the path r₁ = (t,t, 0), 0 ≤ t≤ 1. (Give your answer as a whole or exact number.) So F. dr₁ = Calculate F. dr for the path r2 = (t, t², 0), 0 ≤ t ≤ 1. (Give your answer as a whole or exact number.) [.F. F. dr₂ = Calculate f(Q)-f(P). The point Q is the end point of the both paths r₁ and r₂, Q = r₁ (1) = r₂(1). The point P is the starting point of the both paths r₁ and r2, P= r₁(0) = r₂(0). (Give your answer as a whole or exact number.) S(Q)-f(P) =

Let F = Vf and f = 4x²y - 5z. Calculate F. dr for the path r₁ = (t,t, 0), 0 ≤ t≤ 1. (Give your answer as a whole or exact number.) So F. dr₁ = Calculate F. dr for the path r2 = (t, t², 0), 0 ≤ t ≤ 1. (Give your answer as a whole or exact number.) [.F. F. dr₂ = Calculate f(Q)-f(P). The point Q is the end point of the both paths r₁ and r₂, Q = r₁ (1) = r₂(1). The point P is the starting point of the both paths r₁ and r2, P= r₁(0) = r₂(0). (Give your answer as a whole or exact number.) S(Q)-f(P) =

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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Let F = Vf and f = 4x²y - 5z. Calculate F. dr for the path r₁ = (t,t, 0), 0 ≤ t≤ 1. (Give your answer as a whole or exact number.) So F. dr₁ = Calculate F. dr for the path r2 = (t, t², 0), 0 ≤ t ≤ 1. (Give your answer as a whole or exact number.) [.F. F. dr₂ = Calculate f(Q)-f(P). The point Q is the end point of the both paths r₁ and r₂, Q = r₁ (1) = r₂(1). The point P is the starting point of the both paths r₁ and r2, P= r₁(0) = r₂(0). (Give your answer as a whole or exact number.) S(Q)-f(P) =
Transcribed Image Text:Let F = Vf and f = 4x²y - 5z. Calculate F. dr for the path r₁ = (t,t, 0), 0 ≤ t≤ 1. (Give your answer as a whole or exact number.) So F. dr₁ = Calculate F. dr for the path r2 = (t, t², 0), 0 ≤ t ≤ 1. (Give your answer as a whole or exact number.) [.F. F. dr₂ = Calculate f(Q)-f(P). The point Q is the end point of the both paths r₁ and r₂, Q = r₁ (1) = r₂(1). The point P is the starting point of the both paths r₁ and r2, P= r₁(0) = r₂(0). (Give your answer as a whole or exact number.) S(Q)-f(P) =
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