How to find the limit if integration of polar curves?

[realism877]

Homework Statement

r=3+2cosθ

Homework Equations

The Attempt at a Solution

The text shows that it's from 0 to 2pi.

How did it come to those limits without graphing?

I set r=o. What do I do from there?

 

[vanhees71]

What's the question you want to answer by which integration? If you don't ask a question (also to yourself!) you'll have big trouble to find an answer, because there is no question ;-).

 

[LCKurtz]

Homework Statement

r=3+2cosθ

Homework Equations

The Attempt at a Solution

The text shows that it's from 0 to 2pi.

How did it come to those limits without graphing?

You DO graph it.

 

[realism877]

You DO graph it.

How do you find it on the calculator?

 

[LCKurtz]

How do you find it on the calculator?

How do you find what on a calculator? Graph it with your calculator or by hand.

 

[haruspex]

How do you find it on the calculator?

As vanhees71 says, you need to state the complete problem. You have not provided enough information to find the limits. Are you asked for the area enclosed?

 

[realism877]

As vanhees71 says, you need to state the complete problem. You have not provided enough information to find the limits. Are you asked for the area enclosed?

Find the area of the curve r=3+2cosθ

Find the area it encloses.

 

[hilbert2]

You could first think about a simpler problem, namely finding the area of a rectangle by integration. Suppose one corner of the rectangle is at the origin (0,0) and the opposite corner is at point (a,b). Now the area is

A=\int^{b}_{0}\int^{a}_{0}dxdy

In your problem, we are integrating over a region of (r,$\theta$)-plane. Now you should consider the following questions:

1. What's the equivalent of the area element $dxdy$ in polar coordinates?

2. What are the integration limits in your problem (the upper integration limit when integrating with respect to r coordinate is going to be a function of $\theta$)

 

[haruspex]

Find the area of the curve r=3+2cosθ

Find the area it encloses.

If it encloses an area then there must be two values of theta that produce the same r. Since you only want one copy of the area, you need to find two consecutive such thetas. In general, you might then have to worry whether different consecutive pairs produce different areas, but you should be able to show easily that does not happen here.

 

[LCKurtz]

Regardless of the other suggestions you are receiving, your first step should be to GRAPH IT.