no you didn't. you didn't even integrate correctly
now what?
hmmm I really am not sure. I think what is confusing me is the fact that you have 1 + cos 2 theta. so you have to break the integrals up? and wouldnt this be a u-sub now? with
u = 2theta du = 2 so put 2 in 1/2 out the integral?
hmmm I really am not sure. I think what is confusing me is the fact that you have cos 2 theta. wouldnt this be a u-sub now? with
u = 2theta du = 2 so put 2 in 1/2 out the integral?
but then I get 25/4 sin 2theta
yes...u-sub is the hard way. you should know that , for a constant.
thus you get
now use your trig sub to back substitute to get your answer in terms of .
yes...u-sub is the hard way. you should know that , for a constant.
thus you get
now use your trig sub to back substitute to get your answer in terms of .
ok another probably obvious question. When you have
sin 2 theta how would you go about using substitutions when you dont know what theta is? we know that theta = sin^-1(t/5) but how would that even help here?
ok another probably obvious question. When you have
sin 2 theta how would you go about using substitutions when you dont know what theta is? we know that theta = sin^-1(t/5) but how would that even help here?
did you even read the chapter on trig subs? were you paying attention in class?
since we know , we have the following triangle. use it to find , and then you can change your answer to be in terms of . We find the other side by using Pythagoras' theorem
did you even read the chapter on trig subs? were you paying attention in class?
since we know , we have the following triangle. use it to find , and then you can change your answer to be in terms of
I did read the chapter and have a lot of notes. The trig substitutions section just expects you to know your trig identities which I do not know all of them by heart. I know all the basic identities. The sin2theta I had to look up. Thats what I was confused about.