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CrazyNeutrino
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General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.
and from that, with experience, grows intuition. The latter two aren't sold by weight (in contrast with what some managers seem to think).CrazyNeutrino said:normally just use graph trace
All I can say is usually ##\theta## runs from 0 to ##2\pi## or from ##-\pi## to ##+\pi##. But I doubt if that is helpful for you.CrazyNeutrino said:I find the determination of the limits of integration slightly ambiguous
The limits of integration on polar curves are typically determined by the range of values for the variable θ. This can be determined by looking at the graph of the polar curve and identifying the starting and ending points for θ.
To find the limits of integration for a specific polar curve, you can use the equation for the curve and plug in values for θ to determine the range of values that make up the curve. Alternatively, you can also look at a graph of the curve to visually determine the limits of integration.
Yes, the limits of integration for a polar curve can be negative. This typically occurs when the curve has a portion that extends below the x-axis, resulting in negative values for θ. It is important to consider both positive and negative values when determining the limits of integration for a polar curve.
The limits of integration determine the range of values for which the area under the polar curve is calculated. Changing the limits of integration can result in a different area value, as it includes a different portion of the curve. It is important to ensure that the limits of integration accurately capture the desired area under the curve.
Yes, the limits of integration for a polar curve can change during the integration process. This can occur when the curve has multiple regions with different values for θ. In these cases, the limits of integration will need to be adjusted to accurately capture the entire area under the curve.