What is the value of ∫√(a^2 – x^2) dx | Integrate √(a^2 – x^2) dx. Have a look!!

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**What is the value of ∫√(a^2 – x^2) dx**

Now I’ll integrate

So let’s say that

Thus will be

Next, I’ll simplify it. And that gives

Since , I can say that

Therefore will be

Also, for , will be

Thus will be

Again I know that . Thus will be

So will be

If I integrate it, I get

And is the integration constant.

Now I’ll simplify it to get

Next, I’ll bring back . Since , I can say that

and

Also, will be

Therefore the value of will be

Now I’ll simplify it to get

So I can say

Next, I’ll give some examples on that.

**Solved examples on w****hat is the value of ∫√(a^2 – x^2) dx**

Disclaimer: None of these examples are mine. I have chosen these from some book or books. I have also given the due reference at the end of the post.

So here is the first example.

**Example 1**

According to Stroud and Booth (2013)*, “Evaluate the following:

”

**Solution**

Now here I have to evaluate the expression, say as

First of all, I’ll write it in the form of . So it will be

Next, I’ll rewrite it as

Then I’ll simplify it to get

So becomes

Now I’ll integrate . Also, I’ll use the formula that I’ve mentioned above.

So it will be

where is the integration constant.

Then I’ll simplify it to get

Hence I can conclude that this is the solution to the given example.

Now I’ll give you another example.

**Example 2**

According to Stroud and Booth (2013)*, “Evaluate the following:

”

**Solution**

Now here I have to evaluate the expression, say as

First of all, I’ll write it in the form of . So it will be

Next, I’ll rewrite it as

Then I’ll simplify it to get

So becomes

Now I’ll integrate . Also, I’ll use the formula that I’ve mentioned above.

So it will be

where is the integration constant.

Then I’ll simplify it to get

Hence I can conclude that this is the solution to the given example.

Dear friends, this is the end of today’s post on What is the value of ∫√(a^2 – x^2) dx. 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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