Please send the answers within 1 hour. Thanks. Follow the Steps:
Posted: Mon Jul 11, 2022 11:02 am
Please send the answers within 1 hour. Thanks.
Follow the Steps:
[a] Determine whether or not the vector field F(x, y) = (y e² + siny)i + (e² + x cos y) j is conservative and, if it is, find the potential function. What can be said about the line integral SF F. dr where F is the vector field in part [a] and C is any path connecting the points (1,0) to (2, 1)? [c] Evaluate the line integral in part .
evaluate the line integral. 4. 6.x²6 ² dx + y² dy + z² dz, where C is the curve x + y = 1, .x+ z = 1 from (-2, 3, 3) to (1, 0, 0) 4. With parametric equations C: a = -2+3t, y=3-3t, z = 3-3t, 0≤t≤ 1, for the straight line, = 6,"l² [(-2+ 3t)²(3 dt) + (3-3t)²(-3dt) + (3 - 3t)²(-3 dt)] √_ 2² dx + y² dy + z² dz == = 3 f '((−2+ 3t)² — 2(3 − 3t)²] dt = 3 { -3 { } (- - - 2 1/ (-2+ 3€)³ + ²/ (3 - 3€) ³} 3t)³ 0 -15.
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evaluate the line integral. 4. 6.x²6 ² dx + y² dy + z² dz, where C is the curve x + y = 1, .x+ z = 1 from (-2, 3, 3) to (1, 0, 0) 4. With parametric equations C: a = -2+3t, y=3-3t, z = 3-3t, 0≤t≤ 1, for the straight line, = 6,"l² [(-2+ 3t)²(3 dt) + (3-3t)²(-3dt) + (3 - 3t)²(-3 dt)] √_ 2² dx + y² dy + z² dz == = 3 f '((−2+ 3t)² — 2(3 − 3t)²] dt = 3 { -3 { } (- - - 2 1/ (-2+ 3€)³ + ²/ (3 - 3€) ³} 3t)³ 0 -15.