https://youtu.be/vf_Vk8teH9E

In this video I go over another example on trig integrals and solve the integral of sin(x)<sup>4</sup>. I solve this example by applying the half angle trig identities twice to simplify the integral.

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# Trigonometric Integrals: Example 4

![Trigonometric Integrals Example 4.jpeg](https://cdn.steemitimages.com/DQmTAYQetUafMYaM2SsXEvCfs4E1cGyX9tkg8m3ZZgNfKPS/Trigonometric%20Integrals%20Example%204.jpeg)

**Example:**

![](https://cdn.steemitimages.com/DQmaWJ15SC157Q8DqJyVUjvQAVzXj2bjdR81dHNHSND18Xm/image.png)

**Solution:**

We could evaluate this integral using the reduction formula I covered in my earlier video:

![](https://cdn.steemitimages.com/DQmU5kXNaEzdVPAdKxV2Eg1a6uLpoBMFfydtQ3CUS7WVPRp/image.png)

But a better method is to use the half-angle identity formula:

![](https://cdn.steemitimages.com/DQmcZkbwcW2bxWC6ywXvhbSWdLcydHdZhGjSz4S5JdGnhfK/image.png)

![](https://cdn.steemitimages.com/DQmXqeSQrGyB2N94Uh8XGL8dH6V89qJSLhBZaenjcdd3JPr/image.png)