Question 4 Evaluate the line integral: (i) of T(x) = 4x^3 along the line segment from (-2,1) to (1,2). (ii) where the curve C is parameterized through x(t) = cos t, y(t) = sin t and z = t^2 with tE [0,27T] of S(ydx + xdy + zdz) C (iii) S F(x, y, z) · dr C , where F(x, y, z) = (5z^2 , 2x, x + 2y) and the curve C is given by x = t, y = t^2, and z = t^2 with tE [0,1] %3D

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 4 Evaluate the line integral:
(i) of T(x) = 4x^3 along the line segment from
(-2,1) to (1,2).
(ii) where the curve C is parameterized through
x(t) = cos t, y(t) = sin t and z = t^2 with t E [0,27]
of S(ydx + xdy + zdz) C
(iii) S F(x, y, z) · dr C , where F(x, y, z) = (5z^2 , 2x,
x + 2y) and the curve C is given by x = t, y = t^2,
and z = t^2 with tE [0,1]
Transcribed Image Text:Question 4 Evaluate the line integral: (i) of T(x) = 4x^3 along the line segment from (-2,1) to (1,2). (ii) where the curve C is parameterized through x(t) = cos t, y(t) = sin t and z = t^2 with t E [0,27] of S(ydx + xdy + zdz) C (iii) S F(x, y, z) · dr C , where F(x, y, z) = (5z^2 , 2x, x + 2y) and the curve C is given by x = t, y = t^2, and z = t^2 with tE [0,1]
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