Is there an easier way to do this integral?

[G01]

$$\int_{-1}^1 x^8\sin x dx$$

I know I can do this using integration by parts. But I'd have to do integration by parts 8 times and since I plan on passing calc 2 at the end of this semester I need a quicker way.

If anyone has any hints for me or anything please post them. Thank you for your help.

 

[Hammie]

This may help:

http://www.hyper-ad.com/tutoring/math/int_parts.htm

The method is called tabular integration by parts.

 

[Hammie]

I notice that it is a definite integral. If you know what kind of function this is, there is a real shortcut..

 

[Hurkyl]

As Hammie said, it's often helpful to understand your function! Have you tried anything like plotting it?

 

[G01]

AHHHHHHH! sin(x) is odd! The area under the graph of this function between 1 and -1 is 0! Thanks a lot.