Mathematics and Statistics

Definite Integral

The signed area under a curve between two limits, found from an antiderivative or estimated numerically.

The definite integral of f(x) from a to b is F(b) − F(a), where F is any antiderivative of f. Geometrically it is the area between the curve and the x-axis over that interval, with area below the axis counted as negative. Dividing it by the interval length, b − a, gives the average value of the function.

In engineering it turns a rate into a total: a load diagram into a shear, a hydrograph into a runoff volume, a shape into its area and centroid. When the function is only known at tabulated points, the trapezoidal rule or Simpson’s rule estimates the integral, and Simpson’s rule is exact for polynomials up to a cubic.

How much of the FE Civil exam is Mathematics and Statistics?