Mixing
How to find limits of integration of a parallelogram with these vertices?
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I have to verify Green's theorem for a question with the region being a parallelogram with vertices $(0,0), (1,1),(2,0),(3,1) $ and I'm having trouble with the standard approach of finding limits of integration with Fubini’s Theorem. Now here is where I'm having the problem.
I know that if I'm integrating first with respect to y and then with respect to x, I have to draw a vertical line cutting through the region R in the direction of increasing y and the upper and lower cuts mark the corresponding limits of y as functions of x. I have found x limits to be from 0 to 2 but I'm having a lot of trouble with limits of y.
It seems like the line enters at $y = 0$ and leaves at $y = 1 $. How do you write them as functions of x? Thank you.
I have uploaded a picture to show my attempt and where I got stuck.
My attempt
calculus multivariable-calculus
asked Jan 19 at 9:53
tNotrtNotr
142
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add a comment |
$begingroup$
I have to verify Green's theorem for a question with the region being a parallelogram with vertices $(0,0), (1,1),(2,0),(3,1) $ and I'm having trouble with the standard approach of finding limits of integration with Fubini’s Theorem. Now here is where I'm having the problem.
I know that if I'm integrating first with respect to y and then with respect to x, I have to draw a vertical line cutting through the region R in the direction of increasing y and the upper and lower cuts mark the corresponding limits of y as functions of x. I have found x limits to be from 0 to 2 but I'm having a lot of trouble with limits of y.
It seems like the line enters at $y = 0$ and leaves at $y = 1 $. How do you write them as functions of x? Thank you.
I have uploaded a picture to show my attempt and where I got stuck.
My attempt
calculus multivariable-calculus
asked Jan 19 at 9:53
tNotrtNotr
142
$endgroup$
add a comment |
$begingroup$
I have to verify Green's theorem for a question with the region being a parallelogram with vertices $(0,0), (1,1),(2,0),(3,1) $ and I'm having trouble with the standard approach of finding limits of integration with Fubini’s Theorem. Now here is where I'm having the problem.
I know that if I'm integrating first with respect to y and then with respect to x, I have to draw a vertical line cutting through the region R in the direction of increasing y and the upper and lower cuts mark the corresponding limits of y as functions of x. I have found x limits to be from 0 to 2 but I'm having a lot of trouble with limits of y.
It seems like the line enters at $y = 0$ and leaves at $y = 1 $. How do you write them as functions of x? Thank you.
I have uploaded a picture to show my attempt and where I got stuck.
My attempt
calculus multivariable-calculus
asked Jan 19 at 9:53
tNotrtNotr
142
$endgroup$
I have to verify Green's theorem for a question with the region being a parallelogram with vertices $(0,0), (1,1),(2,0),(3,1) $ and I'm having trouble with the standard approach of finding limits of integration with Fubini’s Theorem. Now here is where I'm having the problem.
I know that if I'm integrating first with respect to y and then with respect to x, I have to draw a vertical line cutting through the region R in the direction of increasing y and the upper and lower cuts mark the corresponding limits of y as functions of x. I have found x limits to be from 0 to 2 but I'm having a lot of trouble with limits of y.
It seems like the line enters at $y = 0$ and leaves at $y = 1 $. How do you write them as functions of x? Thank you.
I have uploaded a picture to show my attempt and where I got stuck.
My attempt
calculus multivariable-calculus
calculus multivariable-calculus
asked Jan 19 at 9:53
tNotrtNotr
142
asked Jan 19 at 9:53
tNotrtNotr
142
edited Jan 20 at 6:22
tNotr
asked Jan 19 at 9:53
tNotrtNotr
142
asked Jan 19 at 9:53
tNotrtNotr
142
asked Jan 19 at 9:53
tNotrtNotr
142
142
add a comment |
add a comment |
1 Answer
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It is something like,
$$int_{y=0}^{1}int_{y}^{y+2} left(...right)dxdy$$
answered Jan 19 at 11:34
Satish RamanathanSatish Ramanathan
10k31323
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1 Answer
1
active
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1 Answer
1
active
oldest
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active
oldest
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active
oldest
votes
$begingroup$
It is something like,
$$int_{y=0}^{1}int_{y}^{y+2} left(...right)dxdy$$
answered Jan 19 at 11:34
Satish RamanathanSatish Ramanathan
10k31323
$endgroup$
add a comment |
$begingroup$
It is something like,
$$int_{y=0}^{1}int_{y}^{y+2} left(...right)dxdy$$
answered Jan 19 at 11:34
Satish RamanathanSatish Ramanathan
10k31323
$endgroup$
add a comment |
$begingroup$
It is something like,
$$int_{y=0}^{1}int_{y}^{y+2} left(...right)dxdy$$
answered Jan 19 at 11:34
Satish RamanathanSatish Ramanathan
10k31323
$endgroup$
It is something like,
$$int_{y=0}^{1}int_{y}^{y+2} left(...right)dxdy$$
answered Jan 19 at 11:34
Satish RamanathanSatish Ramanathan
10k31323
answered Jan 19 at 11:34
Satish RamanathanSatish Ramanathan
10k31323
answered Jan 19 at 11:34
Satish RamanathanSatish Ramanathan
10k31323
answered Jan 19 at 11:34
Satish RamanathanSatish Ramanathan
10k31323
10k31323
add a comment |
add a comment |
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