# Double integral in polar form: how do you find the boundaries?

#### winbacker

Hi I need to use a double integral to find the area of the region bounded by:

r = 3 + 3sinQ where Q = theta.

I know the bounds of the inner integral are from 0 to 3 + 3sinQ.

However, I do not know how to determine the bounds of the outer integral.

Any help would be greatly appreciated.

Related Calculus and Beyond Homework Help News on Phys.org

#### Wretchosoft

The outer integral is just a typical single-variable polar integral. Play with the equation to figure out when the behavior of r begins to repeat itself as theta varies, paying particular attention to the periodic nature of sine. Perhaps a polar graph might help.

Last edited:

#### winbacker

Ok, well I know that once theta = 2pi, the behavior of of sinQ will repeat itself. Should I then plug in 2pi to the equation and work with that?

I know the value of sinQ becomes zero again at pi. Does this mean the outer boundary is from 0 to pi?

#### Mark44

Mentor
0 to pi, although you can exploit the symmetry of the figure by doubling the value you get integrating from 0 to pi/2.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving