Integrate vector fields. Today I will discuss how to integrate vector fields.
Want to know more about integration in vector analysis?? Do check out :
Integrate vector field_compressed
Integrate vector fields
Have a look at this example.
Integrate vector fields – how??
Here I will show a solved example on how to integrate vector fields.
Note: This example is not mine. I have chosen it from some book. I have also given the due reference at the end of the post.
So here is the one.
According to Stroud and Booth (2011)* and determine
Here the two given vectors are and .
First of all, I have to find out the cross product of these two vectors.
I have already discussed earlier how to get the cross product or vector product of two vectors. Here also I will do the same.
Thus will be
Now I will simplify the determinant on the right-hand side. Hence it will be
Now I will find out the value of .
Thus it will be
Now I’ll use the standard procedure if integration. So this gives
Then I’ll simplify it to get
Next, I’ll substitute the limits to get the value of as
As you can see, the only task is now to simplify it. And I’ll also do the same. So that means
and that gives
Now I’ll do a bit more simplification to get the final value of as
Hence I can conclude that the value of is
And this is the answer to the given example.
Dear friends, this is the end of today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!