1. (25 pts] Let F(x, y, z) = (2xy4 +25)i + (4.x²y3 + 2yz3)j + (5x24 + 3y2 -2)k and let C be the curve given parametrically by r(t) = (3t+1)i + t?j + 5tk for 0 <t<1. Evaluate the line integral [F F. dr
1. (25 pts] Let F(x, y, z) = (2xy+ + 25)i + (4x²y3 + 2yz3)j + (5x24 + 3y2z2)k and let C be the curve given parametrically by r(t) = (3t+1)i + tºj + 5tk for 0 <t<1. Evaluate the line integral Sa Spa
Please explain all steps. Thanks! 1. (25 pts) Let F(x, y, z) = (2xy + 25)i + (4.r?y3 + 2yz?)j + (5.624 + 3y222)k and let C be the curve given parametrically by r(t) = (3t+1)i + tºj + 5tk for 0 <t<1. Evaluate the line integral (Fd
good evening. i need help with this calculus question. i will thumbs up your answer. [25 pts) Let F(x, y, z) = (2xy + 2)i + (4x²y3 + 2yz)j + (5224 + 3y²z2)k and let C be the curve given parametrically by r(t) = (3t+1)i + tºj + 5tk for 0 <t<1. Evaluate the line integral [F. '. dr
May you please explain all steps? I want to understand this and am so confused. Thanks! 1. (25 pts) Let F(x, y, z) = (2xy + 25)i + (4.r?y3 + 2yz?)j + (5.624 + 3y222)k and let C be the curve given parametrically by r(t) = (3t+1)i + tºj + 5tk for 0 <t<1. Evaluate the line integral (Fd
Consider F and C below. F(x, y, z) = yze?i + e'?j + xyek, C: r(t) - (t? + 1)i + (t? - 1)j + (t– 3t)k, Osts3 (a) pind a function f such that F – Vf. f(x, y, z) (b) Use part (a) to evaluate F. dr along the given curve C.
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
I lost in this I need help please thank you 13) [6;10] Given F(x, y, z)=(-2yz, y, 3x), and C is the curve of intersection of z = 3x² +3y2 and z=3. Sketch a representative drawing. Assume C has counterclockwise orientation when viewed from above. (a) SET UP the line integral (F. dr as a line integral with a parameter t. Your final integral should be a с single integral in terms of t only, including the bounds of integration....
Use (part A) line integral directly then use (part B) Stokes' Theorem 10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C is the unit circle in the plane z (a) 67 (d) 12m 3. (b) TT (e) None of these (c) 3 TT 10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C...
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 10z) k C is the line segment from (3, 0, -3) to (4, 4, 1) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate [s vf. dr along the given curve C.