Integral of sec??

Question

Integral of sec??

thatonegirl_ · Answer

$$\int\limits_{-\pi/3}^{\pi/3}4\sec \theta \tan \theta    d \theta $$

agent0smith · Answer

Doesn't it look familiar?

thatonegirl_ · Answer

No?

agent0smith · Answer

$$\large 4\int\limits\limits_{-\pi/3}^{\pi/3}\sec \theta \tan \theta    d \theta$$google the derivative of secant.

thatonegirl_ · Answer

The deriv or antideriv?

thatonegirl_ · Answer

ahh ok so its just sec then. Didn't know that. Thank you :)

thatonegirl_ · Answer

Just out of curiosity, how would you take the derivative of secx?

thatonegirl_ · Answer

oh wtf is wrong with me. I know how to do it o.o I'm sorry

thatonegirl_ · Answer

And yes, it is familiar :P

agent0smith · Answer

You can find the derivative of sec x by using the quotient rule with 1/cos x.

You can also evaluate this integral by looking at the graph and noticing it's an odd function. For an odd function...$$\large \int\limits_{-a}^{a}f(x) dx = 0$$

thatonegirl_ · Answer

Thank you very much :D

agent0smith · Answer

$$\large 4\int\limits_{-\pi/3}^{\pi/3}\sec \theta \tan \theta    d \theta= \left[ \sec \theta  \right]_{-\pi/3}^{\pi/3}$$But again, it's an odd function (you can prove it is odd easily by replacing x with -x in sec x tan x)

thatonegirl_ · Answer

What do u mean by odd? :S

agent0smith · Answer

Google odd and even functions Odd function: f(-x) = -f(x) http://archive.cnx.org/resources/cfeb45c70581646aa078b82fc313ea30d467f58d/eo1.gif http://archive.cnx.org/resources/923e29fc3fc1abfe1d2c75eda4b1bd994caf47ff/eo43.gif Even function: f(-x) = f(x) http://www2.bc.cc.ca.us/resperic/Math6A/Lectures/ch1/1/evenodd/evenod1.gif http://archive.cnx.org/resources/cfeb45c70581646aa078b82fc313ea30d467f58d/eo1.gif

thatonegirl_ · Answer

Oh yeah, thanks for that!! You've been really helpful, as always!

agent0smith · Answer

Welcome :)