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some corrections
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pigeon
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Edit 1Edit 1:

Issues seem to emerge from within ImplicitRegion as well as Region Plot. Using $Surd[y^{2},{3}]$ or avoiding $y^{2/3}$ by using $y^{3}$ will result in a correct result of Integrate. Also   Area and Integrate seem to return identical results.

In other case both the results of RegionPlot or Integrate[1,Element[{x,y},reg] of the following ImplicitRegion will be wrongwrong, as verified by last result (In case no mistake was done):

$\text{reg7}=\text{ImplicitRegion}\left[\sin [x]\leq y\leq \cos [x],\left\{\left\{x,0,\frac{3 \pi }{2}\right\},y\right\}\right] $

The results and double checking them unfold as follows:

$\text{RegionPlot}[\text{reg7}]$ enter image description here

$\text{Integrate}[1,\{x,y\}\in \text{reg7}]$

$2 \left(\sqrt{2}-1\right)$

$\int_0^{\frac{3 \pi }{2}} \text{Abs}[ \cos [x]-\sin [x]] \, dx$

$2 \left(2 \sqrt{2}-1\right)$

Original Post:

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]$

$\text{RegionPlot}[\text{reg}]$ enter image description here

$\text{Integrate}[1,y\in \text{reg}]$

$\frac{1}{10}$

$\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

Edit 1:

Issues seem to emerge from within ImplicitRegion as well as Region Plot. Using $Surd[y^{2},{3}]$ or avoiding $y^{2/3}$ by using $y^{3}$ will result in a correct result of Integrate. Also Area and Integrate seem to return identical results.

In other case both the results of RegionPlot or Integrate[1,Element[{x,y},reg] of the following ImplicitRegion will be wrong, as verified by last result (In case no mistake was done):

$\text{reg7}=\text{ImplicitRegion}\left[\sin [x]\leq y\leq \cos [x],\left\{\left\{x,0,\frac{3 \pi }{2}\right\},y\right\}\right] $

The results and double checking them unfold as follows:

$\text{RegionPlot}[\text{reg7}]$ enter image description here

$\text{Integrate}[1,\{x,y\}\in \text{reg7}]$

$2 \left(\sqrt{2}-1\right)$

$\int_0^{\frac{3 \pi }{2}} \text{Abs}[ \cos [x]-\sin [x]] \, dx$

$2 \left(2 \sqrt{2}-1\right)$

Original Post:

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]$

$\text{RegionPlot}[\text{reg}]$ enter image description here

$\text{Integrate}[1,y\in \text{reg}]$

$\frac{1}{10}$

$\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

 

Edit 1:

Issues seem to emerge from within ImplicitRegion as well as Region Plot. Using $Surd[y^{2},{3}]$ or avoiding $y^{2/3}$ by using $y^{3}$ will result in a correct result of Integrate.   Area and Integrate seem to return identical results.

In other case both the results of RegionPlot or Integrate[1,Element[{x,y},reg] of the following ImplicitRegion will be wrong, as verified by last result (In case no mistake was done):

$\text{reg7}=\text{ImplicitRegion}\left[\sin [x]\leq y\leq \cos [x],\left\{\left\{x,0,\frac{3 \pi }{2}\right\},y\right\}\right] $

The results and double checking them unfold as follows:

$\text{RegionPlot}[\text{reg7}]$ enter image description here

$\text{Integrate}[1,\{x,y\}\in \text{reg7}]$

$2 \left(\sqrt{2}-1\right)$

$\int_0^{\frac{3 \pi }{2}} \text{Abs}[ \cos [x]-\sin [x]] \, dx$

$2 \left(2 \sqrt{2}-1\right)$

Original Post:

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]$

$\text{RegionPlot}[\text{reg}]$ enter image description here

$\text{Integrate}[1,y\in \text{reg}]$

$\frac{1}{10}$

$\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

Adding extra results and checkings..
Source Link
pigeon
pigeon
  • 43
  • 6

Edit 1:

Issues seem to emerge from within ImplicitRegion as well as Region Plot. Using $Surd[y^{2},{3}]$ or avoiding $y^{2/3}$ by using $y^{3}$ will result in a correct result of Integrate. Also Area and Integrate seem to return identical results.

In other case both the results of RegionPlot or Integrate[1,Element[{x,y},reg] of the following ImplicitRegion will be wrong, as verified by last result (In case no mistake was done):

$\text{reg7}=\text{ImplicitRegion}\left[\sin [x]\leq y\leq \cos [x],\left\{\left\{x,0,\frac{3 \pi }{2}\right\},y\right\}\right] $

The results and double checking them unfold as follows:

$\text{RegionPlot}[\text{reg7}]$ enter image description here

$\text{Integrate}[1,\{x,y\}\in \text{reg7}]$

$2 \left(\sqrt{2}-1\right)$

$\int_0^{\frac{3 \pi }{2}} \text{Abs}[ \cos [x]-\sin [x]] \, dx$

$2 \left(2 \sqrt{2}-1\right)$

Original Post:

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]$

$\text{RegionPlot}[\text{reg}]$ enter image description here

$\text{Integrate}[1,y\in \text{reg}]$

$\frac{1}{10}$

$\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]$

$\text{RegionPlot}[\text{reg}]$ enter image description here

$\text{Integrate}[1,y\in \text{reg}]$

$\frac{1}{10}$

$\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

Edit 1:

Issues seem to emerge from within ImplicitRegion as well as Region Plot. Using $Surd[y^{2},{3}]$ or avoiding $y^{2/3}$ by using $y^{3}$ will result in a correct result of Integrate. Also Area and Integrate seem to return identical results.

In other case both the results of RegionPlot or Integrate[1,Element[{x,y},reg] of the following ImplicitRegion will be wrong, as verified by last result (In case no mistake was done):

$\text{reg7}=\text{ImplicitRegion}\left[\sin [x]\leq y\leq \cos [x],\left\{\left\{x,0,\frac{3 \pi }{2}\right\},y\right\}\right] $

The results and double checking them unfold as follows:

$\text{RegionPlot}[\text{reg7}]$ enter image description here

$\text{Integrate}[1,\{x,y\}\in \text{reg7}]$

$2 \left(\sqrt{2}-1\right)$

$\int_0^{\frac{3 \pi }{2}} \text{Abs}[ \cos [x]-\sin [x]] \, dx$

$2 \left(2 \sqrt{2}-1\right)$

Original Post:

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]$

$\text{RegionPlot}[\text{reg}]$ enter image description here

$\text{Integrate}[1,y\in \text{reg}]$

$\frac{1}{10}$

$\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

Some cleaning up of bold font that was present...
Source Link
pigeon
pigeon
  • 43
  • 6

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\pmb{\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]}$

$\text{ImplicitRegion}\left[y\leq x\leq y^{2/3}\&\&-1\leq y\leq 1,\{x,y\}\right]$$\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]$

$\pmb{\text{RegionPlot}[\text{reg}]}$$\text{RegionPlot}[\text{reg}]$ enter image description here

$\pmb{\text{Integrate}[1,y\in \text{reg}]}$$\text{Integrate}[1,y\in \text{reg}]$

$\frac{1}{10}$

$\pmb{\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy}$$\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\pmb{\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]}$

$\text{ImplicitRegion}\left[y\leq x\leq y^{2/3}\&\&-1\leq y\leq 1,\{x,y\}\right]$

$\pmb{\text{RegionPlot}[\text{reg}]}$ enter image description here

$\pmb{\text{Integrate}[1,y\in \text{reg}]}$

$\frac{1}{10}$

$\pmb{\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy}$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

I am trying to Integrate the area mentioned below using ImplicitRegion function, following this resource. This method worked in many other scenario. The plot was accurate, but the integration returned 1/10 which is not true as is verified by the traditional integration. I have tried integration over $-1\leq y\leq 0$ and $0\leq y\leq 1$ separately and also using Surd[x,3]^2 but things got much weirder. Can any one give a hint how I can improve or correct this?

$\text{reg}=\text{ImplicitRegion}\left[y\leq x\leq y^{\frac{2}{3}},\{x,\{y,-1,1\}\}\right]$

$\text{RegionPlot}[\text{reg}]$ enter image description here

$\text{Integrate}[1,y\in \text{reg}]$

$\frac{1}{10}$

$\int_{-1}^1 \left(y^{\frac{2}{3}}-y\right) \, dy$

$\frac{3}{5} \left(1+(-1)^{2/3}\right)$

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pigeon
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