# Integral of sec(x)

• Mar 18th 2010, 08:16 PM
s3a
Integral of sec(x)
Is there an intuitive way to do it using integration techniques or do I have to memorize this: integral secx - Wolfram|Alpha ?

Any input would be appreciated!

Edit: Nevermind, I forgot that this is one of the integrals I'm supposed to have memorized as ln|sec(x) + tan(x)|.

Edit #2: Actually, my problem is because of the interval; how do I evaluate this integral over this specific interval?: http://www.wolframalpha.com/input/?i...om+0+to+pi%2F4
• Mar 18th 2010, 09:26 PM
drumist
$\int_0^{\pi / 4} \sec x \, dx = \left[ \ln | \sec x + \tan x | \right]_0^{\pi / 4} = \ln \left| \sec \frac{\pi}{4} + \tan \frac{\pi}{4} \right| - \ln | \sec 0 + \tan 0|$

Don't worry about what Wolfram was giving you. It's just an alternative form of the same value.
• Mar 18th 2010, 09:32 PM
s3a
That's the problem though, sec(pi/4) = 1/cos(pi/4) = 1/0 = BAD
• Mar 18th 2010, 09:35 PM
drumist
Quote:

Originally Posted by s3a
That's the problem though, sec(pi/4) = 1/cos(pi/4) = 1/0 = BAD

No, it's not.

$\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$
• Mar 19th 2010, 07:41 AM
s3a
Quote:

Originally Posted by drumist
No, it's not.

$\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$

I know this is gonna sound nerdy or like I'm in denial or something but when I went to bed last night I was like "Oh s***! pi/4 is not 90deg!" But thanks, that clears everything! :)
• Mar 19th 2010, 08:21 AM
tom@ballooncalculus
Quote:

Originally Posted by s3a
Is there an intuitive way to do it using integration techniques or do I have to memorize this: integral secx - Wolfram|Alpha ?