3. x = y^2, y - x = 2, y = -2, y = 3; ?(x, y) = 1.

Name: 3. x = y^2, y - x = 2, y = -2, y = 3; ?(x, y) = 1.
Uploaded: 2023-02-28T00:39:12-08:00
Duration: 8 min 23 s
Channel: Vincenzo Zaccaro
Description: 3. x = y^2, y - x = 2, y = -2, y = 3; ?(x, y) = 1.

Transcript

00:01 Okay, so let's sketch our region first.

00:04 So this is the x -axis, this is the y -axis.

00:08 Here we have our parabola, x equals y -squared.

00:14 Then we have our line y equals 2 plus x.

00:24 So 2 plus x, which is going to be, this one is 2, 2 plus x, like this one here.

00:34 So this is the line y equals to plus x.

00:40 This one is x equal to negative 2.

00:44 Perfect.

00:44 Then we have y equals negative 2.

00:49 Okay so y equals negative 2.

00:54 Then we have y equal to 3.

00:57 Okay so let's see maybe okay let me fix this parabola.

01:04 Okay.

01:04 So three is here and this is our line perfect so at the end our region is going to be exactly this one here perfect and we have our density which is constant equal to one so let's compute the mass of our lamina okay our mass is going to be what well here we are going to use an integral respect to y basically so here we are gonna have an integral from okay so with respect to y so we are gonna have an integral from negative to two to three okay so three which is this one here so from negative to to three all okay so we have x equals y squared so y squared minus, okay, this line here.

02:12 Okay, this one is the line with equation, x equal to y minus two.

02:18 So y minus two like this in the y, in the y, perfect.

02:25 Okay, let's keep in mind that here we don't even need to write our density because the density is constant and equal to one...

Question

3. x = y^2, y - x = 2, y = -2, y = 3; ?(x, y) = 1.

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