integration problem

**rbenito** · September 14th 2007, 02:55 PM

can anybody help me with this integral ?

(attached as bitmap)

**Soroban** · September 15th 2007, 08:47 AM

Hello, rbenito!

I got a different answer . . .

$\int^{\infty}_0 a\,x\,e^{-a}\,dx$

Integrate by parts . . .

. . $\begin{array}{ccccccc}u & = & x & \quad & dv & = & ae^{-ax}dx \\<br /> du & = & dx & \quad & v & = & -e^{-ax}\end{array}$

We have: . $-xe^{-ax} + \int^{\infty}_0\!\! e^{-ax}dx \;\;=\;\;-xe^{-ax} - \frac{1}{a}e^{-ax}\,\bigg]^{\infty}_0 \;\;=\;\;-\frac{e^{-ax}}{a}(ax + 1)\,\bigg]^{\infty}_0$

. . $= \;\lim_{t\to\infty}\left[-\frac{ax+1}{ae^{ax}}\right]^t_0 \;= \;\lim_{t\to\infty}\left[-\frac{at+1}{ae^{at}} - \left(-\frac{1}{a}\right)\right] \;=\;0 - \left(-\frac{1}{a}\right) \;=\;\frac{1}{a}<br />$

**galactus** · September 15th 2007, 02:26 PM

Hey Soroban.

I believe you're right. I see my mistake.

After looking at it again, I get the same.

Thread: integration problem

LinkBack

Thread Tools

Display

integration problem

Similar Math Help Forum Discussions

Simple Integration problem: Trigonometric Integration

Integration problem

problem in integration

integration problem no.11

integration problem no.10

Search Tags