Mathematics of Computation, Vol. 18, No. 87 (Jul., 1964), pp. 421-432 (12 pages) ...

Differentiation of algebraic and trigonometric expressions can be used for calculating rates of change, stationary points and their nature, or the gradient and equation of a tangent to a curve.

P.S.—I thank Mr. C. F. Merchant for pointing out in NATURE of June 3 that the four-ordinate rule is already in use, and for giving a reference to Tchebycheff's rules, with which I was unacquainted.

G. B. M. Zerr, On the Evaluation of Certain Definite Integrals, The American Mathematical Monthly, Vol. 11, No. 3 (Mar., 1904), pp. 56-62 ...

To calculate the area between a curve and the \(x\)-axis we must evaluate using definite integrals. First, we need to find out where the curve cuts the \(x\)-axis. Remember, a curve cuts the ...