# Thread: how do i do this reverse integration

1. ## how do i do this reverse integration

it is a double integeration

integrate integrate dydx

where my x and y value is

1<x<0

2<y<4-2x

2. Originally Posted by slurm
it is a double integeration

integrate integrate dydx

where my x and y value is

1<x<0 Mr F says: Do you mean -1 < x < 0 ?

2<y<4-2x
First you draw the region defined by the inequalities. Have you done this?

3. yes i done it but it seems i cant attach a picture to show my graph
anyway after sketching

i found out my range changes as it is now dxdy

2<y<4

0<x<[(y-4)/-2]

4. it seems that is is not correct because integration of dxdy should be equal to dydx

5. Originally Posted by slurm
yes i done it but it seems i cant attach a picture to show my graph
anyway after sketching

i found out my range changes as it is now dxdy

2<y<4

0<x<[(y-4)/-2]
You haven't answered my red question.

6. oh no the range for x is 0 and 1, as if like 0 is lower boundary and 1 is upper boundary.. haha if only i could draw it in a text box it will be easier

7. Originally Posted by slurm
oh no the range for x is 0 and 1, as if like 0 is lower boundary and 1 is upper boundary.. haha if only i could draw it in a text box it will be easier
Then it should be evident from your diagram that $\displaystyle \int_{x = 0}^{x = 1} \int_{y = 2}^{y = 4 - 2x} dy \, dx = \int_{y = 0}^{y = 4} \int_{x = 0}^{x = \frac{4 - y}{2}} dx \, dy$.

Also:

Originally Posted by slurm
it is a double integeration
integrate integrate dydx

where my x and y value is

1<x<0 Mr F says: This should be 0 < x < 1.

2<y<4-2x Mr F says: I hope the inequalities here are going the correct way.

8. is this answer? but when i integrate the left side of ur ans i get 2 instead of 1

9. oh no , a mistake in my integration.... sorry,got it already .thx alot

10. yeah got it already, thanks alot another question i would like to ask since i be doing vector calculus

i have a weakness in sketching and finding the limits of the integral. like for example sketching a parabola and such , do u have any tips in sketching graphs

11. Originally Posted by slurm
yeah got it already, thanks alor another question i would like to ask since i be doing vector calculus

i have a weakness in sketching and finding the limits of the integral. like for example sketching a parabola and such , do u have any tips in sketching graphs
Practice. Lots of it.

12. yeah .. alright , i must agree that pressure really makes diamond, although i know nothing about chemistry, alright thanks alot again