Question

Use Green's Theorem to evaluate the line integral along the given positively oriented curve.




integral C (xy^2 dx + 4x^2 y) dy

C is the triangle with vertices (0, 0), (3, 3), and (3, 6)

Answer 1

tried something?

Answer 2

yes I got 48 but it's wrong

Answer 3

let me give you direct calculation instead instead of process.

Answer 4

```
Integrate[D[4 x^2 y, x] - D[x y^2, y], {x, 0, 3}, {y, 0, x}] +
Integrate[D[4 x^2 y, x] - D[x y^2, y], {x, 0, 3}, {y, x, 6 - x}]
```

Answer 5

gives
891/4

Answer 6

woops!! something went wrong

Answer 7

162 ... is that your answer?

Answer 8

http://www.wolframalpha.com/input/?i=Integrate%5BD%5B4+x%5E2+y%2C+x%5D+-+D%5Bx+y%5E2%2C+y%5D%2C+%7Bx%2C+0%2C+3%7D%2C+%7By%2C+0%2C+x%7D%5D+%2B+++Integrate%5BD%5B4+x%5E2+y%2C+x%5D+-+D%5Bx+y%5E2%2C+y%5D%2C+%7Bx%2C3%2C+6%7D%2C+%7By%2C+0%2C+6+-+x%7D%5D

Answer 9

no:S

Answer 10

what does your answer sheet say?

Answer 11

it's a webassign question:S

Answer 12

what about this
http://www.wolframalpha.com/input/?i=Integrate%5BD%5B4+x%5E2+y%2C+x%5D+-+D%5Bx+y%5E2%2C+y%5D%2C+%7By%2C+0%2C+3%7D%2C+%7Bx%2C+0%2C+y%7D%5D+%2B+++Integrate%5BD%5B4+x%5E2+y%2C+x%5D+-+D%5Bx+y%5E2%2C+y%5D%2C+%7By%2C3%2C+6%7D%2C+%7Bx%2C+0%2C+3%7D%5D

Answer 13

425.5??

Answer 14

wrong:S

Answer 15

Ugh!!

Answer 16

http://www.wolframalpha.com/input/?i=Integrate%5BD%5B4+x%5E2+y%2C+x%5D+-+D%5Bx+y%5E2%2C+y%5D%2C+%7Bx%2C+0%2C+3%7D%2C+%7By%2C+x%2C+2x%7D%5D+