SOLUTION: Evaluate: {{{int( sin(2011(2x-3)pi)*(2x-3)^2011, dx, -1,4)}}}

Question 395544: Evaluate:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Let , . We now have

(I'm writing it at an indefinite integral for now. Don't forget the 1/2 at the end)

Letting , , we obtain and

Applying integration by parts,

Which is equal to:

Hopefully, by repeatedly using integration by parts, you should be able to get a sum of 2010 or 2011 terms that should be simplifiable in some way. However the easiest way is obviously to use the nint() function or the definite integral function on a graphing calculator.

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