UsukiDoll
  • UsukiDoll
Sketch the region of integration, reverse the order of integration, and evaluate the integral
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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UsukiDoll
  • UsukiDoll
1 Attachment
UsukiDoll
  • UsukiDoll
this is what I got so far...how do I evaluate this in terms of x when there is a y inside the sin? @wio
UsukiDoll
  • UsukiDoll
Moreover is there a simpler way to find the new values for reversing the integral?

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UsukiDoll
  • UsukiDoll
I feel like I'm treading into unknown waters. except for the dydx ones...since it's type 1 and I have to go from left to right to get type II. It seems that the y values are there when I look in the same direction as bottom to top
UsukiDoll
  • UsukiDoll
@hartnn ???
UsukiDoll
  • UsukiDoll
what I did is in the attachment. It's easier to do it that way rather than drawing it on here
UsukiDoll
  • UsukiDoll
http://assets.openstudy.com/updates/attachments/522e9a27e4b0fbf34d63d88f-usukidoll-1378785914685-14.226.png
hartnn
  • hartnn
what you did is correct.... now first we will be integrating w.r.t x right ? so in sin (xy), 'y' will be treated as constant same as integrating sin (ax)
UsukiDoll
  • UsukiDoll
holy crud I actually got the new integral values correct?
UsukiDoll
  • UsukiDoll
is there any easier way to remember or a tip or something? It's just that part that drives me nuts.
UsukiDoll
  • UsukiDoll
that would be...-cos(ax)
hartnn
  • hartnn
to remember ? nothing to remember.... first you find out the region, here it was, |dw:1378786640140:dw| right ?
UsukiDoll
  • UsukiDoll
yeah
hartnn
  • hartnn
so, previously it was y=x to y=2 (vertical lines) to change the order we just make horizontal lines in same region |dw:1378786772700:dw| that would be x=0 to x=y as you correctly mentioned :)
hartnn
  • hartnn
now since we are FIRST integrating w.r.t x we will treat y as constant so integral of sin (xy) will be -cos (xy)/y don't forget to divide by constant (here y) got this ?
UsukiDoll
  • UsukiDoll
ok now I go tit :) so then it would be F(y)-f(0)
hartnn
  • hartnn
yup, go ahead
UsukiDoll
  • UsukiDoll
-cos(yy)/y - [-cos(0)/y]
UsukiDoll
  • UsukiDoll
|dw:1378786967712:dw|
UsukiDoll
  • UsukiDoll
|dw:1378787010839:dw|
UsukiDoll
  • UsukiDoll
|dw:1378787049911:dw|
UsukiDoll
  • UsukiDoll
and then integrate with respect to y and then F(2)-F(0)
hartnn
  • hartnn
don't forget the 2y^2 which was there before, which you took out of the integral w.r.t x, because it was a constant...remember ?
UsukiDoll
  • UsukiDoll
oh yeah so ...|dw:1378787239080:dw|
hartnn
  • hartnn
|dw:1378787294972:dw|
hartnn
  • hartnn
and 2y^2 will get distribute to both terms
UsukiDoll
  • UsukiDoll
|dw:1378787346996:dw|
hartnn
  • hartnn
yeah, note the 'y' s getting cancelled... then that an easy integral to integrate
UsukiDoll
  • UsukiDoll
|dw:1378787460966:dw|
UsukiDoll
  • UsukiDoll
u=y^2 du = 2y
UsukiDoll
  • UsukiDoll
???
hartnn
  • hartnn
good, go ahead
hartnn
  • hartnn
u= y^2 du = 2ydy
UsukiDoll
  • UsukiDoll
|dw:1378787668981:dw|
hartnn
  • hartnn
corret
hartnn
  • hartnn
but don't forget to change the LIMITS of integration
UsukiDoll
  • UsukiDoll
|dw:1378787745703:dw|
UsukiDoll
  • UsukiDoll
F(2)-F(0)
hartnn
  • hartnn
you can resubstitute back...but i think it will be beter if you had changed the limits, when you did u=y^2
UsukiDoll
  • UsukiDoll
nah I rather resubsitute
hartnn
  • hartnn
ok, so u getting 4-sin4....do you have answer ? is this correct ?
UsukiDoll
  • UsukiDoll
-sin4+4 ???? what the
UsukiDoll
  • UsukiDoll
yup :)
UsukiDoll
  • UsukiDoll
gawd dam**** I must selfesteem issues with the subject or something
hartnn
  • hartnn
correct? so i need not go through it again ?
UsukiDoll
  • UsukiDoll
huh?
UsukiDoll
  • UsukiDoll
I got -sin4+4
hartnn
  • hartnn
i mean i was going through it again, just to make sure all steps were correct...if you had an answer, then there was no need of this
UsukiDoll
  • UsukiDoll
so it's -sin4+4?
UsukiDoll
  • UsukiDoll
o_O
hartnn
  • hartnn
i am checking steps...
hartnn
  • hartnn
yes! -sin 4 +4 is correct :)
UsukiDoll
  • UsukiDoll
yay!!! and i do have self esteem issues with this subject like what the heck I used to fly right through this bt i now i break down every time I solve a problem
UsukiDoll
  • UsukiDoll
:/ plus all the old material is coming back. argh that's what happens when I don't use any calculus material for a semester
hartnn
  • hartnn
good luck :)
UsukiDoll
  • UsukiDoll
thanks :)

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