Question

Why is the integral of cos^2(theta) d(theta) = 1/2(theta) + 1/2sin(theta)cos(theta) + C.

Answer 1

\[\int\limits_{}^{} \cos ^{2} \Theta d \theta = \frac{ 1 }{ 2 }*\theta + \frac{ 1 }{ 2 } \sin \theta \cos \theta +C\]

Answer 2

shouldnt the answer be 1/2(theta + sin(2theta)/2)?

Answer 3

this the intergral that you are talking about \[\int \cos^2\theta d\theta\]

Answer 4

yes

Answer 5

well that's the same answer my friend

Answer 6

it is just some identities manipulation

Answer 7

both are good answers

Answer 8

can you show me? how they are the same???

Answer 9

well what \[\sin 2x=?\]

Answer 10

2sinxcosx

Answer 11

so ?

Answer 12

2/2 cancels right

Answer 13

ya

Answer 14

then you distribute 1/2 and you get the same answer

Answer 15

oh ok :D

Answer 16

i am learning about trigonometric substitution right now, so does it matter which form i use?

Answer 17

no it really doesn't matter! trig integrals always come with couple of different forms lol

Answer 18

ok thanks :D

Answer 19

depends on what you used to integrate! as long as the procedure is correct
you shouldn't worry about the final form

Answer 20

and welcome

Answer 21

Thanks for the advice

Answer 22

anytime!