Question

Sketch the region of integration, reverse the order of integration, and evaluate the integral

Answer 1

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

Answer 2

Moreover is there a simpler way to find the new values for reversing the integral?

Answer 3

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

Answer 4

@hartnn ???

Answer 5

what I did is in the attachment. It's easier to do it that way rather than drawing it on here

Answer 6

http://assets.openstudy.com/updates/attachments/522e9a27e4b0fbf34d63d88f-usukidoll-1378785914685-14.226.png

Answer 7

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)

Answer 8

holy crud I actually got the new integral values correct?

Answer 9

is there any easier way to remember or a tip or something? It's just that part that drives me nuts.

Answer 10

that would be...-cos(ax)

Answer 11

to remember ?
nothing to remember....
first you find out the region, here it was,

right ?

Answer 12

yeah

Answer 13

so, previously it was y=x to y=2 (vertical lines)
to change the order we just make horizontal lines in same region

that would be x=0 to x=y
as you correctly mentioned :)