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The key is to look at the first and second derivatives of that function. Remember that a turning point always has the first derivative equal to zero. Then, the sign of the second derivative indicates if t...

Starting with x=2cosu, rearrange for u to get u=arccos(x/2), then find the upper and lower limits of the integral. We find that our lower limit goes from 1 to pi/3, ad our upper limit goes from root 2 to ...

1/2 *e^(x)(sin x -cos x)