Question

Evaluate the integral:
dx / e^(pie*x) from 2 (upper bound) to 0.

Answer 1

Substitution:
u = - π x
d u = - π d x
d x = - d u / π
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`-1/ \pi \int\limits^2_0 {e ^(u) } \, du =- (e ^(- \pi x) )/( \pi ) = \\ -1/ \pi (e ^(-2 \pi ) -1) = \\ = (1)/( \pi ) - (1)/( \pi e ^(2 \pi ) )`