Use Stokes' Theorem to compute oint_C 1/2 z^2 dx + (xy)dy+2020dz, where C is the triangle with vertices at(1,0,0),(0,2,0), and (0,0,2) traversed in the order.

Isa Trevino 2021-02-05 Answered
Use Stokes' Theorem to compute C12z2dx+(xy)dy+2020dz, where C is the triangle with vertices at(1,0,0),(0,2,0), and (0,0,2) traversed in the order.
You can still ask an expert for help

Want to know more about Green's, Stokes', and the divergence theorem?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

l1koV
Answered 2021-02-06 Author has 100 answers

Step 1
The aim is to find C12z2dx+xydy+2020dz where C is the triangle.
(1, 0, 0), (0, 2, 0), (0, 0, 2).
Step 2
Given the stoke’s theorem,
S curl F.dS=CF.dr
Where S is x1+y2+z2=1
Then curl F=(RyQz)i+(PzRx)j+(QxPy)k
Here F=12Z2i+xyj+2020k
curlF=(RyQz)i+(PzRx)+(QxPy)=zj+yk
If the surface S is,
SF.dS=DP(gx)Q(gy)+RdA
Where F=Pi+Qj+Rk.
Where, z=2y2x.
Then using the stoke's theorem,
S curl F.dS=D2z2=xy+2020dA
Substitute z=2y2x,
CurlFD2+2x+2y2x2ydA
=2DdA
Hence, the area of the triangle is base×height2=12.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-01-06

Use Stokes' Theorem to evaluate CFdr where C is oriented counterclockwise as viewed above.
F(x,y,z)=xyi+3zj+5yk, C is the curve of intersection of the plane x+z=10 and the cylinder x2+y2=9.

asked 2022-03-24

 

asked 2021-03-08
z = x Let be the curve of intersection of the cylinder x2+y2=1 and the plane , oriented positively when viewed from above . Let S be the inside of this curve , oriented with upward -pointing normal . Use Stokes ' Theorem to evaluate ScurlFdSifF=yi+zj+2xk.
asked 2020-12-02
Evaluate the line integral Cxydx+x2dy, where C is the path going counterclockwise around the boundary of the rectangle with corners (0,0),(2,0),(2,3), and (0,3). You can evaluate directly or use Greens
asked 2021-12-17
A camera shop stocks eight different types of batteries, one of which is type A7b.Assume there are at least 30 batteries.
of each type.a. How many ways can a total inventory of 30 batteries be distributed among the eight different types? b.
How many way can a total inventory of 30 batteries be distributed among the eight different types of the inventory must
include at least four A76 batteries?c. How many ways can a total inventory of 30 batteries be distributed among the eight
different types of the inventory includes at most three A7b batteries
asked 2020-12-17
Let F(x,y)=xy2+8x,x2y8y. Compute the flux Fnds of F across a simple closed curve that is the boundary of the half-disk given by x2+y27,y0 using the vector form Greens
asked 2020-10-20
Use Greens