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Q&A Find limits of integration in polar coordinates

2 answers · posted 3y ago by MissMulan‭ · last activity 3y ago by r~~‭

Question calculus double-integrals polar

#2: Post edited by (deleted user) · 2021-08-24T15:41:41Z (about 3 years ago)
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Find limits of integration in polar coordinates

Suppose we have this graph and we want to find the area between the 2 curves:
![hi](https://math.codidact.com/uploads/xum62GPERZqYiqMuiVmgLAq1).
We can calculate the are using a double integral:
~~![hi](https://math.codidact.com/uploads/axR3bn8H6att46y116XAXeUT)~~
~~![hi](https://math.codidact.com/uploads/yk94caT3ihKQs4P9nCVwGWhb)~~
In polar coordinates the equation of the curves take this form:
~~![a](https://math.codidact.com/uploads/odkFguKn7CnqsyLG3QMDFBvY)~~
and
~~![a](https://math.codidact.com/uploads/u7BqhyH2viMsy5AZHBoquKEC)~~
How do I find the limits of integration of the angle theta?

Suppose we have this graph and we want to find the area between the 2 curves:
![hi](https://math.codidact.com/uploads/xum62GPERZqYiqMuiVmgLAq1).
We can calculate the are using a double integral:
![graph](https://math.codidact.com/uploads/axR3bn8H6att46y116XAXeUT)
![equation](https://math.codidact.com/uploads/yk94caT3ihKQs4P9nCVwGWhb)
In polar coordinates the equation of the curves take this form:
![equation](https://math.codidact.com/uploads/odkFguKn7CnqsyLG3QMDFBvY)
and
![equation](https://math.codidact.com/uploads/u7BqhyH2viMsy5AZHBoquKEC)
How do I find the limits of integration of the angle theta?

#1: Initial revision by $user avatar$ MissMulan‭ · 2021-08-24T13:36:10Z (about 3 years ago)

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Find limits of integration in polar coordinates

Suppose we have this graph and we want to find the area between the 2 curves:

![hi](https://math.codidact.com/uploads/xum62GPERZqYiqMuiVmgLAq1).

We can calculate the are using a double integral:

![hi](https://math.codidact.com/uploads/axR3bn8H6att46y116XAXeUT)

![hi](https://math.codidact.com/uploads/yk94caT3ihKQs4P9nCVwGWhb)

In polar coordinates the equation of the curves take this form:

![a](https://math.codidact.com/uploads/odkFguKn7CnqsyLG3QMDFBvY)

and 

![a](https://math.codidact.com/uploads/u7BqhyH2viMsy5AZHBoquKEC)

How do I find the limits of integration of the angle theta?

calculus double-integrals polar

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