the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expressing the antiderivative, all of which...

The integral of secant cubed is a frequent and challenging indefinite integral of elementary calculus: ∫ sec 3 ⁡ x d x = 1 2 sec ⁡ x tan ⁡ x + 1 2 ∫ sec...

Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function can be...

Gudermannian function is typically defined for − ∞ < ψ < ∞ {\textstyle -\infty <\psi <\infty } to be the integral of the hyperbolic secant ϕ = gd ⁡ ψ ≡...

22/7 exceeds π Trapezium rule Integral of the secant function Integral of secant cubed Arclength Solid of revolution Shell integration Natural logarithm...

The external secant function (abbreviated exsecant, symbolized exsec) is a trigonometric function defined in terms of the secant function: exsec ⁡ θ =...

cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and...

the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph of a function...

trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals. For the special...

trigonometric functions, under suitably restricted domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant...

secant "sech" (/ˈsɛtʃ, ˈʃɛk/), hyperbolic cosecant "csch" or "cosech" (/ˈkoʊsɛtʃ, ˈkoʊʃɛk/) corresponding to the derived trigonometric functions. The...

one of its secant lines. The method of exhaustion was later discovered independently in China by Liu Hui in the 3rd century AD to find the area of a circle...

not strictly a transcendental function. Periodic functions Trigonometric functions: sine, cosine, tangent, cotangent, secant, cosecant, exsecant, excosecant...

real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two...

is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It is one of the most important results in real...

zero). The angles λ and φ are expressed in radians. By the integral of the secant function, x = R ( λ − λ 0 ) , y = R ln ⁡ [ tan ⁡ ( π 4 + φ 2 ) ] ...

mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to...

the length of the arc of a circle from the tangent, and vice versa; as also for the secant and logarithmic tangent and secant, and vice versa. These...

the statement that the secant line of a convex function lies above the graph of the function, which is Jensen's inequality for two points: the secant...

inverse hyperbolic secant, and inverse hyperbolic cotangent. They are commonly denoted by the symbols for the hyperbolic functions, prefixed with arc-...

The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral...

The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals...

known as a secant line. If the two points that the secant line goes through are close together, then the secant line closely resembles the tangent line...

Consequently, the secant lines do not approach any single slope, so the limit of the difference quotient does not exist. However, even if a function is continuous...

rational functions the sine and cosine functions (but not tangent, cotangent, secant, or cosecant) the hyperbolic sine and cosine functions (but not hyperbolic...

produced tables of sines, cosines and tangents. Muhammad ibn Jābir al-Harrānī al-Battānī (853–929) discovered the reciprocal functions of secant and cosecant...

the slope of the curve may be approximated by the slope of the secant line between two nearby points. When the curve is given as the graph of an algebraic...

integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative...

characterization of the Cauchy type." Proceedings of the American Mathematical Society, 1976:130–135. Hardy, Michael (2016). "On Tangents and Secants of Infinite...

table of values of the integral of the secant function, and was the essential step needed to make practical both the making and the navigational use of Mercator...