Question

@zepdrix
∫∫e^(x+y) dy dx limits for x<=y<=2x &
-1<=x<=1.

Answer 1

nw x or y which one to take as constant?

Answer 2

In the last problem, our inner integral involved e^(1/y) dy which was a problem. That's why we ended up switch the order, it gave us something more along the lines of e^(x) which was nice to deal with.

In this particular problem, it doesn't appear that the exponential is going to give us any trouble either way we do it, so we'll leave the bound the way they gave them to us.
\[\huge \int\limits_{-1}^{1} \int\limits_x^{2x} e^{x+y} \; dy \; dx\]

Answer 3

In order to simplify this a little bit, we'll need to split up the exponential using rules of exponentials.
Remember how to split it up if we have the sum of the powers? :)

Answer 4

\[\huge \int\limits_{-1}^1 \int\limits_x^{2x}e^x\cdot e^y \quad dy \quad dx\]That make sense? :D

Answer 5

multiply

Answer 6

So again, we have a nice constant, times a very easy exponential,
Think of this as ae^y dy

Answer 7

ok. thanks.

Answer 8

let me work out...

Answer 9

is e ans 2.35

Answer 10

I'm coming up with 3.05, it's quite possible I made a mistake though :) It's a tricky one to simplify.

It's sounds like you're on the right track though ^^ so that's good.

Answer 11

but the ans is..?

Answer 12

yes, i got 3.051

Answer 13

Oh ok cool c:

Answer 14

Depending on who your teacher is, they might prefer that you leave your answers in fraction form. Although this one is quite messy if you do that, so I can't imagine it matters ^^

Answer 15

Sat what time will u be around to ask u some qns. pls...