I have a table `trips` in PostgreSQL 10.5:

```
id  start_date    end_date
----------------------------
1   02/01/2019    02/03/2019
2   02/02/2019    02/03/2019
3   02/06/2019    02/07/2019
4   02/06/2019    02/14/2019
5   02/06/2019    02/06/2019

```

I want to count the number of days in trips that overlap with given weeks. Trips in the table have inclusive bounds. Weeks start on Monday and end on Sunday. The expected result would be:

```
week_of    days_utilized
------------------------
01/28/19    5
02/04/19    8
02/11/19    4

```

For a calendar reference:

```
Monday 01/28/19 - Sunday 02/03/19
Monday 02/04/19 - Sunday 02/10/19
Monday 02/11/19 - Sunday 02/17/19

```

I know how to write this in the programming language I use, but I'd prefer to do this in Postgres and I'm unclear where to start ...