Question

Hi i need help on double integrals, using the change of order . i dont know how to get the reversed limits. please help.

∫∫ (2x-3y) dx dy + ∫∫ (2x-3y) dx dy

first set of limts for dxdy.

the inside integral is from 0 to 2x
The outside integral is from 0 to 2

Second set of limts for dxdy.

the inside integral is from 0 to 4(3-x)
The outside integral is from 2 to 3

Answer 1

this is for the first integral ?

the inside integral is from 0 to 2x
The outside integral is from 0 to 2

so it should by dydx if so

Answer 2

Is it possible for you to show me mate. Because if i do it by dydx i get -16 for the first integral, i checked on wolform alpha and its -16/3

Answer 3

The question states change the order of intregration too?

Answer 4

the thing i say is that it is not possible to have an integral of dxdy
and the limits
the inside integral is from 0 to 2x
The outside integral is from 0 to 2

because then you will be stuck with a 'x' in the solution

Answer 5

how come the answeris -16/3 and i get -16 for the first double integral?

Answer 6

i have left the limits the same.

Answer 7

you have a region and you chose the limits ?

Answer 8

what is given in the question

Answer 9

i got limts 2 to 0 -6x^2 dx which gives -16?

Answer 10

∫∫ (2x-3y) dx dy if you solve this by the limits that you gave me
you would end up with a 'x' in the answer..
please write the question as it is

Answer 11

iam trying to solve the first set of integrals first, then combine it with the second set but im getting -16, when it should be -16/3 for the first set of double integrals. i need to get the first park right before i proceed to the second set of integrals.

Answer 12

you see ∫ (2x-3y) dx from 0 to 2x gives :
x^2 -3xy plug limits : 4x^2 -6xy
now
∫ 4x^2 -6xydy from 0 to 2 gives

4yx^2 -(xy^2)/ 3 plug limits :
8x^2 - (4/3)x

Answer 13

but there is something wrong with the limits you gave

Answer 14

Whats wrong with them?

Answer 15

please write the question again as it is given to you

Answer 16

∫∫ (2x-3y) dx dy + ∫∫ (2x-3y) dx dy

first set of limts for dxdy.

the inside integral is from 0 to 2x
The outside integral is from 0 to 2

Second set of limts for dxdy.

the inside integral is from 0 to 4(3-x)
The outside integral is from 2 to

Answer 17

the limits are not true .. you cant solve it using those limits!

Answer 18

only if the first integral is dydx instead of dxdy it is possible

Answer 19

i will attatch a print screen of question.

Answer 20

only if the first integral is dydx instead of dxdy it is possible

Answer 21

im having problem attaching the file, im new to do this.. website

Answer 22

is it possible that the first integral is dydx instead of dxdy ?

Answer 23

if so :
∫∫ (2x-3y) dy dx using the limits you provided is :
2xy -1.5y^2 from 0 to 2x is :
4x^2 - 6x^2 = -2x^2
∫ -2x^2dx from 0 to 2
(-2/3)x^3 = -16/3

Answer 24

i thnk my lecturer did make a mistake on the question so you dont have to change the order?

Answer 25

if we want to change the order we should be first looking at the region :

Answer 26

is it not x=y/2 to 0 to 4 to 0

Answer 27

if we want to have dxdy instead of dydx we have :

look at what x does ?
goes from y/2 to 2
and then y goes from 0 to 4

Answer 28

i got disconnected

Answer 29

if we want to have dxdy instead of dydx we have :

look at what x does ?
goes from y/2 to 2
and then y goes from 0 to 4

Answer 30

yes i finally got part 1, so you can do it from dxdy after all.

Answer 31

then the integral
∫∫ (2x-3y) dx dy
is :
x^2 -3xy as x goes from y/2 to 2 is
4 - 6y - y^2/4 + 1.5y^2 = 4-6y +1.25y^2
∫4-6y +1.25y^2 dy
4y - 3y^2 + 5y^3/12 from 0 to 4 is
-16/3
the same as we got

Answer 32

yes you can but the first integral is dydx .. (you should understand it because of the limits)

Answer 33

we can change it into dxdy as we did

Answer 34

im on part 2 the second double integrals, for the x i got x=12-y/4 to 3 to y 4 to 0. is that right

Answer 35

the answer? or change or limits ?

Answer 36

for the limits, i got them by a sketch

Answer 37

i can get the answer by dydx thats easy but dxdy i dont understand the change of limits lol!