The discussion revolves around finding the limits of integration for the polar curve defined by r=3+2cosθ. Participants are exploring how to determine these limits without graphing the curve, and there is a focus on understanding the area enclosed by the curve.
The conversation is active with participants seeking clarification on the problem's requirements and the integration limits. Suggestions to graph the curve and consider the area it encloses have been made, but there is no consensus on the approach yet.
Some participants note that the original poster has not provided enough information to fully address the problem, particularly regarding whether the area enclosed by the curve is the focus of the question.
realism877 said: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?
LCKurtz said:You DO graph it.
realism877 said:How do you find it on the calculator?
realism877 said:How do you find it on the calculator?
haruspex said: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?
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.realism877 said:Find the area of the curve r=3+2cosθ
Find the area it encloses.