anonymous
  • anonymous
I'm having a problem with solving this double integral...can someone help me?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Hard to tell if we can't see it ;)
anonymous
  • anonymous
ok there's no way i can put it up like im seeing it because there's integral sign but i'll try my best...
anonymous
  • anonymous
integral 0-2 (integral 0-x/2 5(e)^(x)^2 dy dx)...help me please

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myininaya
  • myininaya
first we integrate inside ignore the outside for right now
myininaya
  • myininaya
since we are integrating with repsect to y we treat everything thats not y ish as a constant
anonymous
  • anonymous
i under stand that. There's no y so I dont understand if i just put a y in there?
myininaya
  • myininaya
what? so you are saying you don't see the inside being 5ye^x^2?
anonymous
  • anonymous
no, there's not a y in the whole problem
myininaya
  • myininaya
whats the antiderivative of 5 with repect to x
anonymous
  • anonymous
0
myininaya
  • myininaya
no
anonymous
  • anonymous
5x?
myininaya
  • myininaya
its 5x since the derivative of 5x is 5
myininaya
  • myininaya
so now you understand how we got 5ye^x^2 for inner integral (we haven't used upper and lower limit yet for inner integral)
anonymous
  • anonymous
ok so you added a y because we were doing respect to y?
myininaya
  • myininaya
yes and the derivative of 5ye^x^2 with respect to y will be 5e^x^2
myininaya
  • myininaya
so the inside integral becomes (5(x/2)e^x^2-0)
myininaya
  • myininaya
now we have the outside integral that we integrating with respect to x
myininaya
  • myininaya
use a substitution for x^2
anonymous
  • anonymous
du/2=x
myininaya
  • myininaya
du/2=x dx yes
myininaya
  • myininaya
dont forget to put the limits in u terms
myininaya
  • myininaya
so the upper limit will be 4 and the lower limit will be 0
myininaya
  • myininaya
so we have int((5/4) *e^u, u=0..4)=(5/4)e^u, u=0..4= (5/4)e^4-(5/4)e^0=(5/4)e^4
myininaya
  • myininaya
-1
myininaya
  • myininaya
i forgot about the minus 1 sorry
myininaya
  • myininaya
e^0=1
anonymous
  • anonymous
thank you very much
myininaya
  • myininaya
np don't be afraid to ask any other questions or this one over if you want
anonymous
  • anonymous
is this a 24 hour website?
anonymous
  • anonymous
on this problem, and when doing substitution is it always required to put the limits in u terms?
myininaya
  • myininaya
i don't know. people come and go as they please. the tutors work whenever they want because we don't work for the website we work because we think its fun lol
myininaya
  • myininaya
if you don't put the limits in terms of u, you have to change it back to x and use the limits for x
anonymous
  • anonymous
is there any way you can explain that?
myininaya
  • myininaya
its the same thing
myininaya
  • myininaya
lets do an example...
anonymous
  • anonymous
this seems like it's going to be a really hard problem
myininaya
  • myininaya
no its not hard i'm just busy doing something else at sametime
myininaya
  • myininaya
pretend we have int(5x,x=0..1)
myininaya
  • myininaya
if we integrate this normal way we get 5x^2/2 x=0..1 = 5/2
myininaya
  • myininaya
we could also do u substitution if we just wanted to for fun so let u=5x
myininaya
  • myininaya
du=5dx => du/5=dx
anonymous
  • anonymous
ok
myininaya
  • myininaya
so we get int(1/5 (u), u=blah blah) =1/5 *u^2/2 let's change this back to x so we will have 1/5*((5x))^2/2 x=0..1 but we could have already done the 5x if we had used u=5x
anonymous
  • anonymous
ok
anonymous
  • anonymous
is it ok to ask another question or should i just retype it on the "ask a question"? you seem to really know your stuff thats why im asking
myininaya
  • myininaya
that didn't answer it?
anonymous
  • anonymous
i mean i have another question.
myininaya
  • myininaya
oh lol yeah I have to do something. I'm fixing to have to move a mattress
anonymous
  • anonymous
ok, thanks for all your help. hope you make lots of money with your math skill one day

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