Hello, this is my teachers notes of how to solve this problem and I do NOT know what the second half of it means. I understand how to do integration by parts up until the step " e^x cosx + integration e^x sinx "
#Calc 2 Repeating integration by parts
manic sleet
upper krakenBOT
Hello, this is my teachers notes of how to solve this problem and I do NOT know ...
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fossil grail
Hello, this is my teachers notes of how to solve this problem and I do NOT know ...
Basically, you express an integral in terms of itself when doing this.
Suppose I = ∫(e^x sin(x) dx). Then we get:
I = e^x (sin(x) - cos(x)) - I
So, you can solve for I here. Just don't forget to also add +C at the end.
manic sleet
Where does e^x sinx come from?
fossil grail
Where does e^x sinx come from?
For the initial integral we have:
u = sin(x), dv = e^x dx
du = cos(x)dx, v = e^x
So, according to the integration by parts formula:
∫(e^x sin(x)dx) = e^x sin(x) - ∫(e^x cos(x)dx)
manic sleet
Ok I see how it gets there. How am I suppoed to know when to do this?
fossil grail
Ok I see how it gets there. How am I suppoed to know when to do this?
Well, do you have any other ideas for this integral? 😅
It's important to know some general ones, then with practice you'll see what to use.
manic sleet
My biggest problem right now is knowing which integration method to use for which problem
This is my first math class in college and we are learning lots of units all at once. I need to know the difference when to use U-Sub, By parts, or Trig substitution and they each have so many cases
fossil grail
I see.
Well, as I said, that mostly comes with practice.
Also, note that some integrals can be solved with different approaches.
manic sleet
Is there one universal way to solve an integral?
fossil grail
No.
manic sleet
Is there a way to check if my answer is correct when integrating by parts?
fossil grail
Of course! Any indefinite integral is easy to check: just differentiate the answer and see if you get the initial function.
manic sleet
How would you check this answer to see if its right
fossil grail
Differentiate (1/2)e^x (sin(x) - cos(x)). If you get e^x sin(x), you at least know that the answer is correct.
runic bone
is help still needed?
manic sleet
i did
now
I added the -integral e^xsinx to the other side now
So ive got
2 integral e^x sinx = e^xsinx - e^xcosx
manic sleet
Ohhh yeah i get it now
runic bone
did you differentiate it?
manic sleet
Yea
runic bone
you got e^x sin(x)?
manic sleet
Yea
manic sleet
Not for now. I think im completely good on Integration by parts but I need to start studying Trig Sub now and im very scared
manic sleet
Should I find a specific problem first?
runic bone
but uh yeah you can close this now
manic sleet
how do i close
manic sleet
+close