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realism877
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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?
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.
The limits of integration for a polar curve are determined by the range of values for the variable theta. These values can be found by looking at the graph of the polar curve and identifying the starting and ending points for theta. Alternatively, you can also solve for the intersections of the curve with the horizontal and vertical axes.
To find the area enclosed by a polar curve, you first need to determine the limits of integration as described above. Then, use the formula A = ½∫(r^2)dθ, where r is the polar function and dθ represents the differential element of theta. Integrate the function between the limits of integration to find the area.
A polar curve is symmetric about the origin if it satisfies the condition r(θ) = r(-θ) for all values of theta. This means that the distance from the origin to a point on the curve is the same as the distance from the origin to the point reflected across the x-axis. You can also determine symmetry by looking at the graph of the polar curve.
Yes, the fundamental theorem of calculus can be used to find the limit of integration for polar curves. This is because the theorem states that the integral of a function can be evaluated by finding its antiderivative and evaluating it between the limits of integration. However, you may need to use the substitution method or other techniques to find the antiderivative of the polar function.
To convert a polar curve into rectangular coordinates, you can use the following formulas: x = rcos(θ) and y = rsin(θ). Simply plug in values for the variable theta to get corresponding values for x and y. Keep in mind that the limits of integration may also need to be adjusted when converting to rectangular coordinates.