How to reconcile the fact that the antiderivative of sin(x) cos(x) has two possible answers?So...
Quintin Stafford
Answered
2022-07-01
How to reconcile the fact that the antiderivative of sin(x) cos(x) has two possible answers? So here is the problem.
This fact doesn't make much sense to me. How do you reconcile the fact that there are two possibilities (notice that these answers aren't only different by a constant)? What are some other functions that have more than one antiderivatives (not only different by a constant)?
Answer & Explanation
Donavan Scott
Expert
2022-07-02Added 22 answers
Explanation: You wrote: (notice that these answers aren't only different by a constant) But they do differ by a constant. If you subtract one solution from the other, you have
which is equal to and using the trig identity , all of this is equal to just which is a constant.