Questions from General Calculus

Q: Use Green’s Theorem to evaluate ∫C F ∙ dr.

Use Green’s Theorem to evaluate ∫C F ∙ dr. (Check the orientation of the curve before applying the theorem.) F (x, y) = 〈e^(-x)+ y^2,e^(-y) x^2 〉, C consists of the arc of the curve y = cos x from (...

Q: Use Green’s Theorem to evaluate ∫C F ∙ dr.

Use Green’s Theorem to evaluate ∫C F ∙ dr. (Check the orientation of the curve before applying the theorem.) F (x, y) =〈y - cos y, x sin y〉, C is the circle (x – 3)2 + (y + 4)2 = 4 oriented clockwise...

Q: Evaluate the line integral. ∫C xy dx + y2

Evaluate the line integral. ∫C xy dx + y2 dy + yz dz, C is the line segment from (1, 0, -1), to (3, 4, 2)

Q: Determine whether or not the vector field is conservative. If it

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. F (x, y, z) = xyz4 i + x2z4 j + 4x2yz3 k

Q: Determine whether or not the vector field is conservative. If it

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. F (x, y, z) = z cos y i + xz sin y j + x cos y k

Q: Verify Green’s Theorem by using a computer algebra system to evaluate both

Verify Green’s Theorem by using a computer algebra system to evaluate both the line integral and the double integral. P (x, y) = 2x - x3y5, Q (x, y) = x3y8, C is the ellipse 4x2 + y2 = 4

Q: Use Green’s Theorem to find the work done by the force F

Use Green’s Theorem to find the work done by the force F (x, y) = x (x + y) i + xy2 j in moving a particle from the origin along the x-axis to (1, 0), then along the line segment to (0, 1), and then b...

Q: A particle starts at the origin, moves along the x-

A particle starts at the origin, moves along the x-axis to (5, 0), then along the quarter-circle x2 + y2 = 25, x > 0, y > 0 to the point (0, 5, and then down the y-axis back to the origin. Use G...

Q: Find a parametric representation for the surface. The plane through

Find a parametric representation for the surface. The plane through the origin that contains the vectors i - j and j - k

Q: Find a parametric representation for the surface. The part of

Find a parametric representation for the surface. The part of the hyperboloid 4x2 - 4y2 - z2 = 4 that lies in front of the yz-plane