The line integral I = F(x, y). dr of the vector field F = (3x², 3y2), where C is the curve given by r(t) = (t(1 – t), sin(xt)), 0 ≤ t ≤ 1,is equal 0; Jc f(x, y, z)ds, where ƒ is a continuous function and C: r = r(t), a ≤ t ≤ b is a smooth curve, does not depend on the parametrization of then curve C; f_cf(x, y, z)ds == fc f(x, y, z)ds, | If F(x, y) = (P(x, y), Q(x, y) and Py = Qx, in an open region D, then F is conservative.
The line integral I = F(x, y). dr of the vector field F = (3x², 3y2), where C is the curve given by r(t) = (t(1 – t), sin(xt)), 0 ≤ t ≤ 1,is equal 0; Jc f(x, y, z)ds, where ƒ is a continuous function and C: r = r(t), a ≤ t ≤ b is a smooth curve, does not depend on the parametrization of then curve C; f_cf(x, y, z)ds == fc f(x, y, z)ds, | If F(x, y) = (P(x, y), Q(x, y) and Py = Qx, in an open region D, then F is conservative.
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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Transcribed Image Text:Which of the following statements are true?
(i) The line integral I = √ F(x, y) ∙ dr of the vector field F = (3x², 3y²), where C is the curve given by r(t) = (t(1 – t), sin(ät)), 0 ≤ t ≤ 1,is equal 0;
(ii) c f(x, y, z)ds, where ƒ is a continuous function and C: r = r(t), a ≤ t ≤ b is a smooth curve, does not depend on the parametrization of then curve C;
(iii) f_c f(x, y, z)ds = − c f(x, y, z)ds,
(iv) If F(x, y) = (P(x, y), Q(x, y) and Py = Qx, in an open region D, then F is conservative.
Only (iii)
b.
Only (ii) and (iv)
c. Only (iii) and (iv)
d. Only (i) and (ii)
e. None of these
a.
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