Step-by-step examples illustrate how to apply both parts of the theorem. You'll see how to evaluate definite integrals using antiderivatives and how the theorem simplifies complex integration problems ...

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.

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 ...