2024-08-29 17-19-28 ก.กำลังสร้าง แคล3เก็บโจทย์+อิทิกรัลเชืงพื้นผิว
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00:00:0054 is the old exam
00:00:05Let me open it
00:00:07The old exam was in 1965
00:00:10and the old exam was in 1955
00:00:14around 1955-1954
00:00:18But in 1954, 55 was written
00:00:22and it was the same exam, the same form, everything was the same
00:00:26and it was the same form, the same form, everything was the same
00:00:29but it was changed from the writing form to the grammar form
00:00:33during the COVID-19
00:00:35There are two types of the cross
00:00:37The cross is closed
00:00:40but the cross is open
00:00:42so the cross can do the green
00:00:44but the cross can't
00:00:46So let's answer the 2.2
00:00:49that the cross can do the green
00:00:53From the Green Theorem, this formula is the function
00:00:58F.dr
00:01:00is equal to the indicate function
00:01:03on the cross path
00:01:05in R
00:01:07Q by Qx minus P by Qy
00:01:10the area
00:01:15PQ has the property
00:01:17P by Qy is equal to
00:01:21Q by Qx is conservative
00:01:29conservative
00:01:32I'll write it in brackets
00:01:34If it's not equal, P by Qy is not equal to
00:01:37Q by Qx is non-conservative
00:01:51What?
00:01:53What?
00:01:59Oh, it's in English
00:02:01Right?
00:02:03It's the same
00:02:07Now
00:02:09I'll change it to English
00:02:11Now, it says
00:02:14Green Theorem is true
00:02:18If it's true
00:02:20I've tried it
00:02:22It's too long
00:02:24because I have to do it in a straight line
00:02:26equal to the green
00:02:28It's too long
00:02:30I'll do only the green
00:02:32I'll do it in a straight line
00:02:34to make it equal to the green
00:02:36It's a waste of time
00:02:38It has the property
00:02:40F by PQ
00:02:43Right?
00:02:45It's the same as the 2.2
00:02:50The 2.2 is the chicken coop
00:02:54That's it
00:02:56Let's start
00:02:58Let's check the green
00:03:00P by Qy
00:03:02Q by Qx
00:03:04conservative
00:03:08P by Qy
00:03:10is negative 2y
00:03:12Q by Qx
00:03:16is 2y
00:03:18It's negative 2 and 0
00:03:20Right?
00:03:22It's not equal
00:03:24If it's not equal
00:03:26F is non-conservative
00:03:32vector field
00:03:34F is non-conservative
00:03:44If it's not equal
00:03:46We enter the Green Theorem
00:03:56The Green Theorem
00:03:58indicates
00:04:00The Green Theorem
00:04:02indicates
00:04:06The Green Theorem
00:04:08indicates
00:04:10Q by Qx
00:04:12negative
00:04:14P by Qy
00:04:16the area
00:04:18Q by Qx
00:04:28Q by Qx
00:04:300
00:04:32negative 2
00:04:34dA
00:04:36It's 2 times
00:04:38the area
00:04:40Right?
00:04:42It's 2 times
00:04:44the area
00:04:46It's 2 times the area
00:04:48It's 2 times the area
00:04:50It's 2 times the area
00:04:52Think about the area
00:04:54plus the area
00:04:56plus the area
00:04:58and put it in
00:05:00right?
00:05:02This is the first Laplacian
00:05:04It's the first Laplacian
00:05:06It's the first Laplacian
00:05:08Let's check the area
00:05:10It's long
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