If I used the method of adding a straight line, would the line integral of the curve of the ellipse be the integral of the curl of the surface minus the integral of the straight line?
Homework Statement
Evaluate the line integral
I = (x2z + yzexy) dx + xzexy dy + exy dz
where C is the arc of the ellipse r(t) = (cost,sint,2−sint) for 0 <= t <= PI.
[Hint: Do not compute this integral directly. Find a suitable surface S such that C is a part of the boundary ∂S and use...
Homework Statement
You must find the time it takes to accelerate (at constant applied torque) a motorcycle from 0 to 100 km/hr,
given:
Rider mass: 75 kg
Bike total mass: 190 kg
Torque at crankshaft of motor: 105 Nm
Front and rear wheel masses (10 kg and 17 kg respectively)
Radius of...
Homework Statement
A vector field F for which div F = 0, is called incompressible (also called solenoidal). Consider the vector field F(x, y, z) = ⟨y, x + y, −z⟩.
(a) (1 point) Show that F is incompressible.
(b) (3 points) Find a vector field A such that F=\nabla×A.Homework Equations
div F =...