- #1
Emspak
- 243
- 1
1. evaluate the following:
[itex]\int^{1}_{0}[/itex][itex]\int[/itex][itex]^{1}_{0}[/itex]xyex+y dydx
OK, so this should be pretty simple. But for some reason I am having trouble integrating the yex+y bit with respect to y. If I do it by parts I end up with iterations like this:
[itex]\int^{1}_{0}[/itex]xyex+y - [itex]\int^{}_{}[/itex]ex+yxdy dx
And integrating again I got
[itex]\int^{1}_{0}[/itex]xyex+y - ex+yx [itex]|^{1}_{0}[/itex] dx plugging in the relevant values I got
[itex]\int^{1}_{0}[/itex]xex+1-xex+1 - xex + xexdx
which with the latter terms cancelling gets you [itex]\int^{1}_{0}[/itex]xex+1-xex+1 dxAnd the whole thing should go to zero.
OK, did I do this whole bit correctly? I want to make sure that I am not doing something stupid. If I did it right, wonderful. (I know this might sound kind of silly to post a problem that I think I did correctly, but it never hurts to have another pair of eyes)
[itex]\int^{1}_{0}[/itex][itex]\int[/itex][itex]^{1}_{0}[/itex]xyex+y dydx
The Attempt at a Solution
OK, so this should be pretty simple. But for some reason I am having trouble integrating the yex+y bit with respect to y. If I do it by parts I end up with iterations like this:
[itex]\int^{1}_{0}[/itex]xyex+y - [itex]\int^{}_{}[/itex]ex+yxdy dx
And integrating again I got
[itex]\int^{1}_{0}[/itex]xyex+y - ex+yx [itex]|^{1}_{0}[/itex] dx plugging in the relevant values I got
[itex]\int^{1}_{0}[/itex]xex+1-xex+1 - xex + xexdx
which with the latter terms cancelling gets you [itex]\int^{1}_{0}[/itex]xex+1-xex+1 dxAnd the whole thing should go to zero.
OK, did I do this whole bit correctly? I want to make sure that I am not doing something stupid. If I did it right, wonderful. (I know this might sound kind of silly to post a problem that I think I did correctly, but it never hurts to have another pair of eyes)