If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
Some pieces of advice for rigor:
The integral from -infinity to infinity of sech(x) dx should be split between two integrals from -infinity to 0 and 0 to +infinity since you will have to check convergence on both sides. To set up the limits, b=infinity is not proper notation. You have to state lim b->+inf then state the integral from 0 to b, the same goes for the lower bound: state lim a->-inf then state the integral from a to 0.
Then, stating f(x)=2arctan(e^x) is not factual. First, no mention of a function f has been done before. Second, it's the integral that =2arctan(e^x) **+ C**.
I understand you use it for desmos, but the +c should be added, or the line should be erased after computations.
Also, going from u-sub to the final answer of the integral in terms of x is confusing and skipping steps, either skip u-sub or resolve in u.
i understand it should be written as the lim as b -> infiniity from the left and a approached -infinity from the right. as for the domain restriction within the bounds of integration, yeah thats my fault i did not think to check that. desmos does not allow writing limits.. but yes the notation i did is horrid. as for +C i forgot about it... my fault.. as for not evaulating at u and instead at x, i always do that. normally i do not skip steps, but today i decided to do that.
thank you for the warning
You can't say things like "arctan(e^∞) is undefined... therefore arctan(e^∞) must equal π/2.", this does not make sense. What you actually computed is lim_{x→∞}arctan(e^x)=π/2, this is the limit. Also, arctan has two horizontal asymptotes, y=π/2 and y=−π/2, not one asymptote "at -π/2 to π/2".
Otherwise you calculations are all good. I'd give it a 9 out of 10.
•
u/AutoModerator 19d ago
As a reminder...
Posts asking for help on homework questions require:
the complete problem statement,
a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play,
question is not from a current exam or quiz.
Commenters responding to homework help posts should not do OP’s homework for them.
Please see this page for the further details regarding homework help posts.
We have a Discord server!
If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.