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Geometrically, when the scalar field f is defined over a plane (n = 2), its graph is a surface z = f(x, y) in space, and the line integral gives the (signed) cross-sectional area bounded by the curve and the graph of f. See the animation to the right.
The blue area above the x-axis may be specified as positive area, while the yellow area below the x-axis is the negative area. The integral of a real function can be imagined as the signed area between the x {\displaystyle x} -axis and the curve y = f ( x ) {\displaystyle y=f(x)} over an interval [ a , b ].
A definite integral of a function can be represented as the signed area of the region bounded by its graph and the ... such as finding the area under a curve, or ...
Important subclasses of convex curves include the closed convex curves (the boundaries of bounded convex sets), the smooth curves that are convex, and the strictly convex curves, which have the additional property that each supporting line passes through a unique point of the curve. Bounded convex curves have a well-defined length, which can be ...
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry, a circular segment or disk segment (symbol: ⌓) is a region of a disk [1] which is "cut off" from the rest of the disk by a straight line.
The area between a positive-valued curve and the horizontal axis, measured between two values a and b (b is defined as the larger of the two values) on the horizontal axis, is given by the integral from a to b of the function that represents the curve: [1]
In topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides the plane into an "interior" region bounded by the curve (not to be confused with the interior of a set) and an "exterior" region containing all of the nearby and far away exterior points.
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Species–area curve; See also. Gallery of curves; List of curves topics;