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00:00:00Most of the points will be added at the end because it's difficult, right?
00:00:04This is going to be a two-tiered indicate.
00:00:10Okay, today we're going to study the Green Theorem in the Plane.
00:00:20The Green Theorem says that Mr. Green
00:00:25The Green Theorem says that if F
00:00:34That's weird.
00:00:36The Green Theorem says that we can change the indicate line to be double.
00:01:02When F is a non-conservative closed path
00:01:26Non-conservative
00:01:36Green Theorem in the Plane
00:01:56Non-conservative
00:02:26Green Theorem in the Plane
00:02:40Non-conservative
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00:07:26Non-conservative
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00:08:22Green Theorem in the Plane
00:08:52Non-conservative
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00:26:11Non-conservative
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00:26:39Non-conservative
00:26:53Non-conservative
00:27:07Non-conservative
00:27:35Non-conservative
00:27:37Non-conservative
00:27:39Non-conservative
00:27:41Non-conservative
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00:28:11Non-conservative
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00:28:39Non-conservative
00:28:41Non-conservative
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00:29:01Non-conservative
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00:29:25Non-conservative
00:29:27Non-conservative
00:29:29Non-conservative
00:29:31Non-conservative
00:29:33Non-conservative
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00:29:37Non-conservative
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00:29:41Non-conservative
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00:29:57Non-conservative
00:30:01Non-conservative
00:30:05Non-conservative
00:30:11Non-conservative
00:30:25Non-conservative
00:30:33Non-conservative
00:30:41TopCase 0-1, the answer is 2-4-2
00:30:47Let's save the answer
00:30:54This is C2
00:31:02If you don't have enough space, you can open a new page
00:31:05Because GeneTool did half of the work
00:31:07GeneTool did only a little bit
00:31:09The answer is C3-5-5
00:31:33Anyone haven't finished C2?
00:31:35The answer is C3
00:32:05The answer is C3
00:32:35How to walk?
00:32:37Walk like this
00:32:39Walk from 0 to 90
00:32:452
00:32:47Dip
00:32:49Dx is equal to DipCross
00:32:51Dx is equal to DipCross
00:32:53Dx is equal to DipCross
00:32:55Dx is equal to DipCross
00:32:57Dx is equal to DipCross
00:32:59Let's set C3
00:33:03Let's print
00:33:06F.dr
00:33:08is equal to
00:33:11C3-2ydx
00:33:13plus 2ydy
00:33:16is equal 0-90
00:33:22Desec 2T
00:33:24Desec Tdt
00:33:26plus 2y
00:33:28Y is side t, dy is cos t dt.
00:33:59This can be fixed.
00:34:03This is 2 sides cos, right?
00:34:052 sides a, cos a, what is it?
00:34:09It is 2 sides a, 2 sides t. This is the formula.
00:34:142 sides t, cos t.
00:34:16Indicate that 2 sides don't use the formula.
00:34:28Use the integral.
00:34:302 sides change to 1 minus cos 2t divided by 2.
00:34:34Integral.
00:34:36This is the integral.
00:34:411 minus cos 2t divided by 2.
00:34:442 minus cos 2t divided by 2.
00:34:50The back side can be replaced by u.
00:34:52The back side can be replaced by u.
00:34:55Replace u with 2t.
00:34:57Dipside can be 2.
00:35:03The front side, indicate 1, get t.
00:35:05Indicate cos can be minus, what is it?
00:35:09Indicate cos can be sine.
00:35:11Don't forget the 2.
00:35:15Replace u with 2t.
00:35:17This is also replacing u with 2t.
00:35:19This is also replacing.
00:35:21Indicate sine can be minus cos 2t.
00:35:34Sine 0.
00:35:40It must be sine pi first.
00:35:45Sine pi.
00:35:57Cos pi.
00:36:05Minus minus is plus.
00:36:07Cos 0.
00:36:11Cos pi can be minus 1.
00:36:14Cos 0 can be minus 2.
00:36:16Plus 1.
00:36:18Cos 0 can be minus 1.
00:36:20Plus 1.
00:36:22Cos 0 can be minus 1.
00:36:24Plus 1.
00:36:26Cos 0 can be minus 2.
00:36:28Plus 1.
00:36:32This is C3.
00:36:38Indicate closed path.
00:36:44C1 plus C2 plus C3.
00:36:48Sum up the numbers.
00:36:50C1 plus C2 plus C3.
00:36:54I forgot C1.
00:36:58C2 minus 2.
00:37:02C3 plus 1.
00:37:06The answer is 2 plus 2.
00:37:13I got the answer.
00:37:15I don't know if I got it right.
00:37:17This is the correct way.
00:37:19I just got the correct way.
00:37:21I just finished the correct way.
00:37:37Is it enough?
00:37:39If it's not enough,
00:37:41I can do another one.
00:37:43It's the same way.
00:37:49Is it worth 15 points?
00:37:51I still don't know
00:37:53whether it's correct or not.
00:37:55If I think about it,
00:37:57it's not the same as the correct way.
00:37:59This is the end.
00:38:03I have to make the correct way
00:38:05equal to the correct way.
00:38:07If I think about it,
00:38:09I don't know if I got it right.
00:38:11I still can't remember the answer.
00:38:13I haven't done it for a long time.
00:38:19Let me take this picture.
00:38:21We can draw it again.
00:38:23Because we have to use the picture
00:38:27to calculate the Green Theorem.
00:38:31Let me think about it.
00:38:33Let's draw it again.
00:38:39Let's draw it again.
00:38:55Let's draw it again.
00:38:57Because we have to use the picture.
00:39:09Let's draw it again.
00:39:29Let's draw it again.
00:39:31Let's draw it again.
00:39:33If you use the same picture,
00:39:35you don't have to.
00:39:37If you use the same picture,
00:39:39you don't have to.
00:40:07If you use the same picture,
00:40:09you don't have to.
00:40:37If you use the same picture,
00:40:39you don't have to.
00:40:41If you use the same picture,
00:40:43you don't have to.
00:40:45If you use the same picture,
00:40:47you don't have to.
00:40:49If you use the same picture,
00:40:51you don't have to.
00:40:53If you use the same picture,
00:40:55you don't have to.
00:40:57If you use the same picture,
00:40:59you don't have to.
00:41:01If you use the same picture,
00:41:03you don't have to.
00:41:05If you use the same picture,
00:41:07you don't have to.
00:41:09If you use the same picture,
00:41:11you don't have to.
00:41:29Green theorem in the plane
00:41:35Green indicates that the line C F dot D R is equal to the two-tiered indicate in R.
00:41:46Q by x minus P by y is equal to D A.
00:41:55Q by x is equal to 0. P by y is equal to negative 2.
00:42:05Q by x is equal to 0. P by y is equal to negative 2.
00:42:35Q by x is equal to 0. P by y is equal to 0.
00:42:45Q by x is equal to 0. P by y is equal to 0.
00:42:55Q by x is equal to 0. P by y is equal to 0.
00:43:05Q by x is equal to 0. P by y is equal to 0.
00:43:15Q by x is equal to 0. P by y is equal to 0.
00:43:25Q by x is equal to 0. P by y is equal to 0.
00:43:35Q by x is equal to 0. P by y is equal to 0.
00:43:45Q by x is equal to 0. P by y is equal to 0.
00:43:55Q by x is equal to 0. P by y is equal to 0.
00:44:05Q by x is equal to 0. P by y is equal to 0.
00:44:15Q by x is equal to 0. P by y is equal to 0.
00:44:25Q by x is equal to 0. P by y is equal to 0.
00:44:35Q by x is equal to 0. P by y is equal to 0.
00:44:45Q by x is equal to 0. P by y is equal to 0.
00:44:55Q by x is equal to 0. P by y is equal to 0.
00:45:05Q by x is equal to 0. P by y is equal to 0.
00:45:15Q by x is equal to 0. P by y is equal to 0.
00:45:25Q by x is equal to 0. P by y is equal to 0.
00:45:35Q by x is equal to 0. P by y is equal to 0.
00:45:45Q by x is equal to 0. P by y is equal to 0.
00:45:55Q by x is equal to 0. P by y is equal to 0.
00:46:05Q by x is equal to 0. P by y is equal to 0.
00:46:15Q by x is equal to 0. P by y is equal to 0.
00:46:25Q by x is equal to 0. P by y is equal to 0.
00:46:35Q by x is equal to 0. P by y is equal to 0.
00:46:45Q by x is equal to 0. P by y is equal to 0.
00:46:55Q by x is equal to 0. P by y is equal to 0.
00:47:05Q by x is equal to 0. P by y is equal to 0.
00:47:15Q by x is equal to 0. P by y is equal to 0.
00:47:25Q by x is equal to 0. P by y is equal to 0.
00:47:35Q by x is equal to 0. P by y is equal to 0.
00:47:45Q by x is equal to 0. P by y is equal to 0.
00:47:55Q by x is equal to 0. P by y is equal to 0.
00:48:05Q by x is equal to 0. P by y is equal to 0.
00:48:15Q by x is equal to 0. P by y is equal to 0.
00:48:25Q by x is equal to 0. P by y is equal to 0.
00:48:35Q by x is equal to 0. P by y is equal to 0.
00:48:45Q by x is equal to 0. P by y is equal to 0.
00:48:55Q by x is equal to 0. P by y is equal to 0.
00:49:05Q by x is equal to 0. P by y is equal to 0.
00:49:15Q by x is equal to 0. P by y is equal to 0.
00:49:25Q by x is equal to 0. P by y is equal to 0.
00:49:35Q by x is equal to 0. P by y is equal to 0.
00:49:45Q by x is equal to 0. P by y is equal to 0.
00:49:55Q by x is equal to 0. P by y is equal to 0.
00:50:05Q by x is equal to 0. P by y is equal to 0.
00:50:15Q by x is equal to 0. P by y is equal to 0.
00:50:35Q by x is equal to 0. P by y is equal to 0.
00:50:55F of x, y is equal to 3x to the power of 2y plus x to the power of 3x.
00:51:15F is not a vector field.
00:51:41Green theorem in the plane.
00:52:01Indicate closed path F dot dr.
00:52:213x to the power of 2y plus 1y is equal to 9.
00:52:31Minus 1 is equal to 1.
00:52:41Minus 1 is equal to 1.
00:53:01Minus 1 is equal to 1.
00:53:21Minus 1 is equal to 1.
00:53:41Minus 1 is equal to 1.
00:54:01Minus 1 is equal to 1.
00:54:21Minus 1 is equal to 1.
00:54:41Minus 1 is equal to 1.
00:55:01Minus 1 is equal to 1.
00:55:21Minus 1 is equal to 1.
00:55:41Indicate closed path F dot dr.
00:56:11F of x, y is equal to 0.
00:56:31Minus 1 is equal to 1.
00:56:51Minus 1 is equal to 1.
00:57:11Minus 1 is equal to 1.
00:57:31Minus 1 is equal to 1.
00:57:51Minus 1 is equal to 1.
00:58:11Minus 1 is equal to 1.
00:58:31Minus 1 is equal to 1.
00:58:41Minus 1 is equal to 1.
00:58:51Minus 1 is equal to 1.
00:59:11Minus 1 is equal to 1.
00:59:21Minus 1 is equal to 1.
00:59:31Minus 1 is equal to 1.
00:59:51Minus 1 is equal to 1.
01:00:11Minus 1 is equal to 1.
01:00:31Minus 1 is equal to 1.
01:00:51Minus 1 is equal to 1.
01:01:11Minus 1 is equal to 1.
01:01:31Minus 1 is equal to 1.
01:01:51Minus 1 is equal to 1.
01:02:11Minus 1 is equal to 1.
01:02:31Minus 1 is equal to 1.
01:02:51Minus 1 is equal to 1.
01:03:11Minus 1 is equal to 1.
01:03:31Minus 1 is equal to 1.
01:03:51Minus 1 is equal to 1.
01:04:11Minus 1 is equal to 1.
01:04:31Minus 1 is equal to 1.
01:04:51Minus 1 is equal to 1.
01:05:11Minus 1 is equal to 1.
01:05:31Minus 1 is equal to 1.
01:05:51Minus 1 is equal to 1.
01:06:11Positive Orientation
01:06:31P x Y and Q x X
01:06:59P x Y and Q x X
01:07:29P x Y and Q x X
01:07:49P x Y and Q x X
01:08:09P x Y and Q x X
01:08:29P x Y and Q x X
01:08:49P x Y and Q x X
01:09:09P x Y and Q x X
01:09:29P x Y and Q x X
01:09:49P x Y and Q x X
01:10:19P x Y and Q x X
01:10:39P x Y and Q x X
01:10:59P x Y and Q x X
01:11:19P x Y and Q x X
01:11:39P x Y and Q x X
01:11:59P x Y and Q x X
01:12:19P x Y and Q x X
01:12:39P x Y and Q x X
01:12:59P x Y and Q x X
01:13:19P x Y and Q x X
01:13:39P x Y and Q x X
01:13:59P x Y and Q x X
01:14:19P x Y and Q x X
01:14:39P x Y and Q x X
01:14:59P x Y and Q x X
01:15:19P x Y and Q x X
01:15:39P x Y and Q x X
01:15:59P x Y and Q x X
01:16:19P x Y and Q x X
01:16:39P x Y and Q x X
01:16:59P x Y and Q x X
01:17:19P x Y and Q x X
01:17:39P x Y and Q x X
01:17:59P x Y and Q x X
01:18:19P x Y and Q x X
01:18:39P x Y and Q x X
01:18:59P x Y and Q x X
01:19:19P x Y and Q x X
01:19:39P x Y and Q x X
01:19:59P x Y and Q x X
01:20:19P x Y and Q x X
01:20:39P x Y and Q x X
01:20:59P x Y and Q x X
01:21:19P x Y and Q x X
01:21:39P x Y and Q x X
01:21:59P x Y and Q x X
01:22:19P x Y and Q x X
01:22:39P x Y and Q x X
01:22:59P x Y and Q x X
01:23:19P x Y and Q x X
01:23:39P x Y and Q x X
01:23:59P x Y and Q x X
01:24:19P x Y and Q x X
01:24:39P x Y and Q x X
01:24:59P x Y and Q x X
01:25:19P x Y and Q x X
01:25:39P x Y and Q x X
01:25:49P x Y and Q x X
01:25:59P x Y and Q x X
01:26:19P x Y and Q x X
01:26:29P x Y and Q x X
01:26:39P x Y and Q x X
01:26:59P x Y and Q x X
01:27:19P x Y and Q x X
01:27:39P x Y and Q x X
01:27:59P x Y and Q x X
01:28:19P x Y and Q x X
01:28:39P x Y and Q x X
01:28:49P x Y and Q x X
01:28:59P x Y and Q x X
01:29:19P x Y and Q x X
01:29:39P x Y and Q x X
01:29:59P x Y and Q x X
01:30:19P x Y and Q x X
01:30:29P x Y and Q x X
01:30:49P x Y and Q x X
01:31:09P x Y and Q x X
01:31:29P x Y and Q x X
01:31:49P x Y and Q x X
01:32:09P x Y and Q x X
01:32:29P x Y and Q x X
01:32:49P x Y and Q x X
01:33:09P x Y and Q x X
01:33:29P x Y and Q x X
01:33:49P x Y and Q x X
01:34:09P x Y and Q x X
01:34:29P x Y and Q x X
01:34:49P x Y and Q x X
01:35:09P x Y and Q x X
01:35:29P x Y and Q x X
01:35:49P x Y and Q x X
01:36:09P x Y and Q x X
01:36:29P x Y and Q x X
01:36:49P x Y and Q x X
01:37:09P x Y and Q x X
01:37:29P x Y and Q x X
01:37:49P x Y and Q x X
01:38:09P x Y and Q x X
01:38:29P x Y and Q x X
01:38:49P x Y and Q x X
01:39:09P x Y and Q x X
01:39:29P x Y and Q x X
01:39:49P x Y and Q x X
01:39:59P x Y and Q x X
01:40:09P x Y and Q x X
01:40:29P x Y and Q x X
01:40:49P x Y and Q x X
01:41:09P x Y and Q x X
01:41:29P x Y and Q x X
01:41:49P x Y and Q x X
01:41:59P x Y and Q x X
01:42:19P x Y and Q x X
01:42:39P x Y and Q x X
01:42:59P x Y and Q x X
01:43:19P x Y and Q x X
01:43:39P x Y and Q x X
01:43:59P x Y and Q x X
01:44:19P x Y and Q x X
01:44:39P x Y and Q x X
01:44:59P x Y and Q x X
01:45:19P x Y and Q x X
01:45:39P x Y and Q x X
01:45:59P x Y and Q x X
01:46:19P x Y and Q x X
01:46:39P x Y and Q x X
01:46:59P x Y and Q x X
01:47:19P x Y and Q x X
01:47:39P x Y and Q x X
01:47:59P x Y and Q x X
01:48:19P x Y and Q x X
01:48:39P x Y and Q x X
01:48:59P x Y and Q x X
01:49:19P x Y and Q x X
01:49:39P x Y and Q x X
01:49:59P x Y and Q x X