https://youtu.be/8KASYak_u2g

In this video I go further into symmetry in integrals by going over 2 useful examples. One of the examples is integrating an even function and the other one is integrating an odd function. Using the concept of symmetry we can greatly simplify the integration so make sure to watch this video!

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# Symmetry in Integrals Examples

![Symmetry in Integrals Examples.jpeg](https://files.peakd.com/file/peakd-hive/mes/PIogHrsw-Symmetry20in20Integrals20Examples.jpeg)

## Recap on Integrals of Symmetric Functions Theorem

Suppose f is continuous on [-a, a].

(a) If f is even, meaning f(-x) = f(x), then:

![image.png](https://files.peakd.com/file/peakd-hive/mes/OqcxkUx9-image.png)

(b) If f is odd, meaning f(-x) = - f(x), then:

![image.png](https://files.peakd.com/file/peakd-hive/mes/iZbdoKM2-image.png)

## Examples 

![image.png](https://files.peakd.com/file/peakd-hive/mes/lHNuzZFk-image.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/Eyq8In7S-image.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/bGgRui1B-image.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/zYHTae2E-image.png)