Answer:
Step-by-step explanation:
Given that:
Here C is the curve of intersection of the hyperbolic parabolic and the cylinder
Using Stokes' Theorem
From above ;
S = the region under the surface and above the circle
Suppose, we consider
therefore, S will be the level curve of f(x,y,z) = 0
Recall that:
is always normal to the surface S at the point (x,y,z).
∴
This implies that the unit vector
So
Also,
Similarly ;
Then:
converting the integral to polar coordinates
This implies that:
⇒
Therefore, the value of
The parametric equations for the curve of intersection of the hyperbolic paraboloid can be expressed as the equations of the plane and cylinder in parametric form . i.e
Set them equal now,
the Parametric equation of