Integral-limit and ?!!.... - Math Help Forum

$Math Help Forum$

$Go Back$		Math Help Forum > University Math Help > Calculus
$Reload this Page$ Integral-limit and ?!!....

Download MHF Flyer

Mark Forums Read

$Reply$

#1

$Old$ June 27th, 2009, 11:56 PM

$dhiab's Avatar$

dhiab $dhiab is offline$

Senior Member

Join Date: May 2009

Location: ALGERIA

Posts: 478

Country:

Algeria

Thanks: 134

Thanked 26 Times in 21 Posts

$dhiab is on a distinguished road$

$Default$ Integral-limit and ?!!....

Calculate this integral :

deduct :

$Reply With Quote$

Advertisement

#2

$Old$ June 28th, 2009, 12:28 AM

$CaptainBlack's Avatar$

$CaptainBlack is offline$

Grand Panjandrum

Join Date: Nov 2005

Location: South of England

Posts: 12,280

Country:

United Kingdom

Thanks: 779

Thanked 4,004 Times in 3,229 Posts

$CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$ $CaptainBlack has a reputation beyond repute$

$Default$

Quote:

Originally Posted by dhiab $View Post$

Calculate this integral :

deduct :

$\int_{2n\pi}^{(2n+1)\pi} e^{-x}\cos(x)\ dx = \text{Re}\int_{2n\pi}^{(2n+1)\pi} e^{-x}e^{ix}\ dx=$ $\text{Re}\int_{2n\pi}^{(2n+1)\pi} e^{(-1+i)x}\ dx =$ $\text{Re} \left[\frac{e^{(-1+i)x}}{-1+i} \right]_{2n\pi}^{(2n+1)\pi}$

and if you do things right you will find this is proportional to $e^{-2n\pi}$ , which will immediate answer the next part, and then the series is geometric.

CB

Last edited by CaptainBlack; June 28th, 2009 at 12:49 AM.

$Reply With Quote$

$Reply$

« The MVT. | Top | An infinite sum »

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are Off

Forum Jump

All times are GMT -7. The time now is 09:45 AM.

your link here Sponsors

rv solar, e-learning,

Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.