Stroke's Theorem  Be Socialized And Subscribed
 Be Socialized And Subscribed
Recive All Latest And Hottest Articles,Tips And Tricks,Awesome Widgets Directly Into Your Inbox And Stay UpDate With Us...!!!  Like Us On FaceBookFollow Us On Twitter  Add Me In CircleSubscribe Our RSS

E-Mail Will Be Delivered By FeedBurner.
cheakout our partner sites Swissen Blog on Security & Technology,  php.swissen.in for Hd PHP Video Tutorial Learning    p.swissen.in for Photoshop Video Tutorial Learning  : admin Top 5

Coming Soon .......

Recent ones
Coming Soon .......  3.219.167.194

ec2-3-219-167-194.compute-1.amazonaws.com

browser info:
CCBot/2.0 (https://commoncrawl.org/faq/)

# Stroke's Theorem

### Introduction :

This theorem states that the line integral of a vector field A around a closed curve is equal to the surface integral of the curl of A taken over the surface S surrounded by the closed curve. ### Proof : consider a surface S enclsed in a vectorfieldA. as shown in figure the boundary of surface S is closed curve PQR.The line integral A around the curve PQR traced counter-clockwise is Let the entire surface be divided into a large number of square loops. let the area enclosed by each infinite small loop be dS suppose be a unit positive outward normal upon dS. The vector area of the element is We know that the curl of a vector field at any point is maximum line integral of the vector computed per unit area along the boundary of an infinitesimal area at that point. So the line integral of A around the boundary of the area dS is this applies to all surface elements.Hence the sum of line integral of A around the boundaries of all the area element is given by This is the surface integral of A.

The sum of the line integrals on the boundary line of curve is given by the above equatons Hence This is Strokes Theorem.