another integration problem

**Sambit** · October 21st 2010, 09:29 AM

evaluate $\int_0^1(\int_x^1 \frac{e^{-y}}{y} dy) dx$

**Ackbeet** · October 21st 2010, 09:33 AM

Change the order of integration. Makes things much easier! Draw the region carefully to get the new limits.

**Sambit** · October 21st 2010, 09:13 PM

if we reverse the order of $dx$ and $dy$ , the integration becomes $\int_0^1(\int_0^y \frac{e^{-y}}{y} dx) dy$
so the final answer comes to be $1 - \frac{1}{e}$ . thanks

**Ackbeet** · October 22nd 2010, 02:06 AM

You're welcome. Have a good one!

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