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# Evaluate the definite integral. $\displaystyle \int^{\pi/3}_{-\pi/3} x^4 \sin x \, dx$

## 0

Integrals

Integration

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

given this function we know what we can actually do is evaluate f of negative ecstasy of its even odd. So everywhere you would have positive acts. I want you to plug in negative acts. Simplify. Okay. As we can see, half of negative X is equivalent to negative aftereffects. Therefore, dysfunction has rotational symmetry about the origin which is zero comma zero. And on top of that, the function is also odd. Which means that because it is odd, we know this and to roll is equivalent to zero. This is the theory that list in the textbook. Therefore, we have the same thing instead of a negative A. We have pie over three and negative pi over three. Therefore, we know the solution to this problem is zero.

#### Topics

Integrals

Integration

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp