Question

Evaluate the integral

Answer 1

\[\int\limits_{0}^{\pi/4} \sec \Theta \tan \Theta d \Theta \]

Answer 2

i think i've used the wrong theta sign.. but yea..those are just theta

Answer 3

Hmm this is an identity that you will become fairly familiar with. But if you're just learning it now, let's do it the proper way. :)
Change everything to sines and cosines, and we'll then look to see if we can apply a nice u-substitution.
Do you remember secant and tangent in sine cosine form? :D

Answer 4

I just know the antiderivative is sec theta

Answer 5

so i'm thinking is sec (pi/4) - sec (0)

Answer 6

oh, and this section is particularly for calculus fundamental theorem

Answer 7

Oh you do know that integral :) ok cool.
So from here, it's probably easier to switch the secants to 1/cos's, then we can try to remember our special angles.

Answer 8

yep, i got sec pi/4 as sqrt (2), but im not sure about sec 0

Answer 9

\[\cos(\pi/4)=\frac{ \sqrt2 }{ 2 }\]\[\sec(\pi/4)=\frac{ 1 }{ \cos(\pi/4) }=\frac{ 2 }{ \sqrt2 }=\sqrt2\]So you were able to find this point ok? c: good good. Just gotta remember the cosine of 0 for the next one.
\[\cos(0)=1\]\[\sec(0)=\frac { 1 }{ \cos(0) }=\frac{ 1 }{ 1 }=1\]
Sorry for slow response :( Open study crashed and made me type this all out again >:c

Answer 10

oh.. i thought sec 0 will be -1.. cuz i'm thinking u need to flip signs.. umm, i get it now, thanks!