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JamesGold
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That is, adding up the differential changes in angle between two arbitrarily chosen points on a function, to find the total change in angle between the tangent lines of those two points. How can this be done?
Charles49 said:The dx is just there to tell you that the integration is done with respect to x. Can you attach a picture so I know what angle you are interested in?
Integration is a mathematical process used to find the area under a curve. In this case, it is used to find the total change in angle between two tangent lines by calculating the integral of the derivative of the function at the points where the tangent lines intersect the curve.
Finding the total change in angle between two tangent lines is important because it allows us to understand the overall change in direction of a curve. This can be useful in various fields such as physics, engineering, and economics.
Yes, integration can be used to find the total change in angle between two non-linear tangent lines. However, the process may be more complex as it involves finding the integral of a non-linear function.
One limitation is that integration requires a continuous function, so it may not be applicable in cases where the curve is discontinuous. Additionally, the process may be more challenging for complex functions or when the points of intersection are not known.
Integration can be applied to real-world problems in various fields such as determining the change in direction of a moving object, analyzing the curvature of a road or track, or calculating the change in slope of a demand or supply curve in economics.