I'm having a problem with solving this double integral...can someone help me?

- anonymous

I'm having a problem with solving this double integral...can someone help me?

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

Hard to tell if we can't see it ;)

- 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

integral 0-2 (integral 0-x/2 5(e)^(x)^2 dy dx)...help me please

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- myininaya

first we integrate inside ignore the outside for right now

- myininaya

since we are integrating with repsect to y we treat everything thats not y ish as a constant

- anonymous

i under stand that. There's no y so I dont understand if i just put a y in there?

- myininaya

what? so you are saying you don't see the inside being 5ye^x^2?

- anonymous

no, there's not a y in the whole problem

- myininaya

whats the antiderivative of 5 with repect to x

- anonymous

0

- myininaya

no

- anonymous

5x?

- myininaya

its 5x since the derivative of 5x is 5

- 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

ok so you added a y because we were doing respect to y?

- myininaya

yes and the derivative of 5ye^x^2 with respect to y will be 5e^x^2

- myininaya

so the inside integral becomes (5(x/2)e^x^2-0)

- myininaya

now we have the outside integral that we integrating with respect to x

- myininaya

use a substitution for x^2

- anonymous

du/2=x

- myininaya

du/2=x dx yes

- myininaya

dont forget to put the limits in u terms

- myininaya

so the upper limit will be 4 and the lower limit will be 0

- 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

-1

- myininaya

i forgot about the minus 1 sorry

- myininaya

e^0=1

- anonymous

thank you very much

- myininaya

np don't be afraid to ask any other questions or this one over if you want

- anonymous

is this a 24 hour website?

- anonymous

on this problem, and when doing substitution is it always required to put the limits in u terms?

- 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

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

is there any way you can explain that?

- myininaya

its the same thing

- myininaya

lets do an example...

- anonymous

this seems like it's going to be a really hard problem

- myininaya

no its not hard i'm just busy doing something else at sametime

- myininaya

pretend we have int(5x,x=0..1)

- myininaya

if we integrate this normal way we get 5x^2/2 x=0..1 = 5/2

- myininaya

we could also do u substitution if we just wanted to for fun so let u=5x

- myininaya

du=5dx => du/5=dx

- anonymous

ok

- 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

ok

- 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

that didn't answer it?

- anonymous

i mean i have another question.

- myininaya

oh lol yeah I have to do something. I'm fixing to have to move a mattress

- anonymous

ok, thanks for all your help. hope you make lots of money with your math skill one day

Looking for something else?

Not the answer you are looking for? Search for more explanations.