Integrate Sin^(n) x. Hello friends, today I’ll show how to integrate Sin^(n) x. Have a look!!

If interested, read more on similar topics like:

**Reduction formula for algebraic functions**

**Example 1 – Integrate Sin^(n) x**

So now I’ll integrate . Therefore I’ll give it a name, say, . So I say,

Also, it has another name. And that is the reduction formula for . As I can see, it’s not possible to integrate straight away. So I’ll try some other way.

**Step 1**

Thus I can write as . And that will help me in integration like

Now I’ll use the * integration by parts* method. And that says

So in this case, I’ll choose as and as . If , then If , then

Thus becomes

Next, I’ll simplify it to get

Also, I can rewrite as

Thus becomes

Then I’ll simplify it. And that gives

(1)

Now comes my next step.

**Step 2**

As I can see, I can’t integrate further. If , then will be

Thus equation (1) becomes

Now I’ll simplify it to get

So I can say that

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

**Example 2**

Get the value of

**Solution**

From the above-mentioned example, I already know that

Now I’ll substitute the limits. So here is the lower limit and is the upper limit. Thus the value of will be

As we all know

So becomes

And that gives

Thus the value of is

Hence I can conclude that this is the solution 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!!

## Leave a Reply