Integrate vector fields. Today I will discuss how to integrate vector fields.

Want to know more about integration in vector analysis?? Do check out :

**The line integral of a scalar field**

Integrate vector field_compressed

**Integrate vector fields**

Integration of vector fields is similar to the **differentiation of vector fields**. It happens when the vector has a parametric form like . Also, it follows the **standard rules of integration**.

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.

**Example **

According to Stroud and Booth (2011)* and determine

**Solution**

Here the two given vectors are and .

First of all, I have to find out the cross product of these two vectors.

**Step 1**

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 .

**Step 2**

Let’s say

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!!

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