Corrected paramateric_region_list and the tests using the method

[ghost]

References to other Issues or PRs

Fixes #20748

Brief description of what is fixed or changed

The paramteric_region_method was earlier substituting tan (t) rather that tan(t/2) , when parametrizing ImplicitRegion object to ParametricRegion objects. This resulted in the value of final computed answer becoming twice of what it should have been, as can be seen from the OP.

Other comments

The earlier tests had wrong answers, this pr fixes them also.

Release Notes

• vector
  • Fixed a bug with integral over ImplicitRegion objects

[sympy-bot]

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• vector
  • Fixed a bug with integral over ImplicitRegion objects (#20867 by @almighty123789)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.8.

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#### References to other Issues or PRs
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Fixes #20748 


#### Brief description of what is fixed or changed
The paramteric_region_method  was earlier substituting `tan (t)` rather that `tan(t/2)`  , when parametrizing ImplicitRegion object to ParametricRegion objects. This resulted in the value of final computed answer becoming twice of what it should have been, as can be seen from the OP.

#### Other comments
The earlier tests had wrong answers, this pr fixes them also.

#### Release Notes

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https://github.com/sympy/sympy/wiki/Writing-Release-Notes for more information
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<!-- BEGIN RELEASE NOTES -->
- vector 
  - Fixed a bug with integral over ImplicitRegion objects
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[friyaz]

Thanks for making this PR @almighty123789. This looks good to me. Just improve the release notes.

[ghost]

@friyaz thanks for commenting and reviwing the PR. Can you tell me what more should I add to the release notes ? Thanks.

[friyaz]

How about "Fixed a bug with integral over ImplicitRegion objects?

[friyaz]

Thanks, I do not have merging rights yet. @oscarbenjamin Can you merge this please if it looks good to you?

[asmeurer]

@friyaz I have given you push access. Please read https://github.com/sympy/sympy/wiki/Pushing-patches.

[friyaz]

Thanks, @asmeurer for this!