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...

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

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...

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

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

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...

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

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

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 ) ] ...

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...

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...

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

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...

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 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...

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 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...

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

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...

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...

maximum at small x. Hence, the integral of a bell-shaped function is typically a sigmoid function. Bell shaped functions are also commonly symmetric...

real-valued functions of several real variables, this holds if and only if the absolute value of the slopes of all secant lines are bounded by K. The set of lines...

The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change...

\theta )\,d\theta .\end{aligned}}} One may evaluate the integral of the secant function by multiplying the numerator and denominator by ( sec ⁡ θ + tan ⁡ θ...