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Topic: List of integrals of trigonometric functions

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Sine integral

List of integrals of irrational functions

Table of integrals

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	Trigonometry Encyclopedia
		The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.
		The trigonometric functions are periodic, with a period of 360 degrees or 2π radians.
		The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.
	www.hallencyclopedia.com /topic/Trigonometry.html (0 words)

	Elliptic Integrals and Elliptic Functions
		The elliptic integrals have a complicated structure in the complex plane.
		Ordinary trigonometric functions are singly periodic, in the sense that
		The inverse Jacobi elliptic functions are related to elliptic integrals.
	documents.wolfram.com /v5/TheMathematicaBook/AdvancedMathematicsInMathematica/MathematicalFunctions/3.2.11.html (0 words)

	Integrals of Trigonometric Functions
		Here is a list of some of them.
		Not to keep you in suspense, here are the antiderivatives of all six trigonometric functions.
		(We will add the constant of integration after we are done.) Notice that we have ended up with the same integral on the right as the one we started with.
	people.hofstra.edu /Stefan_Waner/trig/trig4.html (390 words)

	List of reference tables Details, Meaning List of reference tables Article and Explanation Guide
		This is a list of reference tables, similar to the collection of reference tables found at the back of almanacs, dictionaries and encyclopedias (or an index of them, if they're scattered throughout the work).
		List of mean centers of U.S. population during the 20th century
		List of monasteries dissolved by Henry VIII of England
	www.e-paranoids.com /l/li/list_of_reference_tables.html (1023 words)

	Integral
		In particular, for a constant function, the integral is defined as its constant value times the measure of the region on which it is defined; in this basic case, the integral is just the area of a rectangle (in one dimension) or volume of a prism or cylinder (in two dimensions).
		Its integral is the size of the area bounded by the x-axis and the graph of a function, f(x); negative areas are possible.
		Functions which have antiderivatives are also Riemann integrable (and hence Lebesgue integrable.) The nonobvious theorem that states that the two approaches ("area under the curve" and "antiderivative") are in some sense the same as the fundamental theorem of calculus
	www.guajara.com /wiki/en/wikipedia/i/in/integral.html (1184 words)

	Wikipedia: Integral
		In particular, for a constant function, the integral is defined as its constant value times the measure of the region on which it is defined; in this basic case, the integral is just the area of a rectangle (in one dimension) or volume of a prism or cylinder (in two dimensions).
		Its integral is the size of the area bounded by the x-axis and the graph of a function, f(x); negative areas are possible.
		Functions which have antiderivatives are also Riemann integrable (and hence Lebesgue integrable.) The nonobvious theorem that states that the two approaches ("area under the curve" and "antiderivative") are in some sense the same as the fundamental theorem of calculus
	www.factbook.org /wikipedia/en/i/in/integral.html (0 words)

	List of trigonometric identities Summary
		The trigonometric functions are a set of functions that are employed in the study of angles and angular relationships in planar and 3-dimensional figures.
		An important application is the integration of non-trigonometric functions: a common trick involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
		The fact that the differentiation of trigonometric functions (sine and cosine) results in linear combinations of the same two functions is of fundamental importance to many fields of mathematics, including differential equations and fourier transformations.
	www.bookrags.com /List_of_trigonometric_identities (2114 words)

	Trigonometric function
		Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle.
		The sine and the cosine functions, for example, are used to describe the simple harmonic motion, which models many natural phenomena, such as the movement of a mass attached to a spring and, for small angles, the pendular motion of a mass hanging by a string.
		Trigonometric functions also prove to be useful in the study of general periodic functions.
	libraryoflibrary.com /E_n_c_p_d_Sine.html (7796 words)

	PlanetMath: reduction of elliptic integrals to standard form
		Were this not the case, we could simply pull the repeated factor out of the radical and be left with a polynomial of degree of 1 or 2 inside the square root and express the integral in terms of inverse trigonometric functions.
		"reduction of elliptic integrals to standard form" is owned by rspuzio.
		This is version 11 of reduction of elliptic integrals to standard form, born on 2006-12-10, modified 2006-12-12.
	planetmath.org /encyclopedia/ReductionOfEllipticIntegralsToStandardForm.html (313 words)

	Wikinfo \| Integral
		for a constant function, the integral is defined as its constant value times the measure of the region on which it is defined;
		the integral is just the area of a rectangle (in one dimension) or volume of a prism or cylinder (in two dimensions).
		the size of the area bounded by the x-axis and the graph of a function, f(x); negative areas are possible.
	www.wikinfo.org /wiki.php?title=integral (0 words)

	Trigonometry and Basic Functions - Numericana
		The list is quite literally endless, but we may attempt the beginning of a classification for those functions which are common enough to have a universally accepted name.
		Alternately, such functions may be construed as univalued (ordinary) functions of a variable whose domain is a so-called Riemann surface for which several points may have the same projection on the complex plane.
		Each of those 6 trigonometric functions is the ratio of two sides in a right triangle where one of the acute angles is specified.
	home.att.net /~numericana/answer/functions.htm (4134 words)

	Circular Trigonometric Functions
		Each of the circular trigonometric functions inherits from the exponential function a modulus of periodicity of 2 pi, except that the tangent and cotanget have a modulus of periodicity of pi.
		Lacking the glyph for the integral sign, we are going to indicate the definite integral of a function f(x) with respect to x on the interval from a to b as int(f(x), x, a, b); the indefinite integral as int(f(x), x).
		The values of the inverse circular trigonometric functions have to be obtained from that of the foregoing arctangent, by solving the quadratic equations of the identities and
	www.rism.com /Trig/circular.htm (1932 words)

	PlanetMath: A lecture on trigonometric integrals and trigonometric substitution
		A lecture on trigonometric integrals and trigonometric substitution
		The most usual integrals which involve trigonometric functions can be solved using the identities above.
		This is version 1 of A lecture on trigonometric integrals and trigonometric substitution, born on 2006-01-31.
	planetmath.org /encyclopedia/ALectureOnTrigonometricIntegralsAndTrigonometricSubstitution.html (400 words)

	Integrals of Trigonometric Functions
		Since integrals are antiderivatives, we can read the table backwards and arrive at six basic trig integrals.
		Now that we know what integrals produce the six basic trig functions, we would like to know how to find the integrals of the six basic trig functions.
		The trick to find this integral is to use the sin over cos definition of the tan.
	www.ltcconline.net /greenl/courses/116/IntegrationTechnique/trigIntegrals.htm (284 words)

	Evaluation of the rotation matrices in the basis of real spherical harmonics. (Site not responding. Last check: )
		Rotation matrices (or Wigner D functions) are the matrix representations of the rotation operators in the basis of the spherical harmonics.
		Once again, the expressions of integrals in terms of these functions are simpler than those in terms of the RSH, due to their cartesian tensorial character.
		The Wigner D functions are well known in the quantum theory of angular momentum [5], and their properties can be easily found in the literature.
	www.elsevier.com /homepage/saa/eccc3/paper48/eccc3.html (2838 words)

	Maxima Manual: 20. Integration
		Generally speaking, Maxima only handles integrals which are integrable in terms of the "elementary functions" (rational functions, trigonometrics, logs, exponentials, radicals, etc.) and a few extensions (error function, dilogarithm).
		This procedure may be numerically unstable for a great variety of reasons, but is reasonably fast: avoid using it on highly oscillatory functions and functions with singularities (poles or branch points in the region).
		The QUADPACK functions included in Maxima are all automatic, in the sense that these functions attempt to compute a result to a specified accuracy, requiring an unspecified number of function evaluations.
	maxima.sourceforge.net /docs/manual/en/maxima_20.html (0 words)

	33: Special functions
		Special functions are just that: specialized functions beyond the familiar trigonometric or exponential functions.
		Functions with an addition formula (F(x+y)=P(F(x),F(y)) P a polynomial) are elliptic functions
		Formal definition of the sine function (via integrals) and derivation of some of its properties.
	www.math.niu.edu /~rusin/known-math/index/33-XX.html (611 words)

	Colby \| Course Catalogue \| Mathematics
		Integral calculus of one and several variables; infinite series.
		Vectors, lines, and planes; limits, continuity, derivatives, and integrals of vector-valued functions; polar, spherical, and cylindrical coordinates; partial and directional derivatives; multiple integrals; line and surface integrals; Green's Theorem; Stokes's Theorem; Fourier series; applications.
		The properties of analytic functions, including Cauchy's integral theorem and formula, representation by Laurent series, residues and poles, and the elementary functions.
	www.colby.edu /catalogue/0102/listing/MAlist.shtml (0 words)

	AP: Calculus AB
		Although the exam is based on the topics listed here, teachers may wish to enrich their courses with additional topics.
		Appropriate integrals are used in a variety of applications to model physical, biological, or economic situations.
		Whatever applications are chosen, the emphasis is on using the integral of a rate of change to give accumulated change or using the method of setting up an approximating Riemann sum and representing its limit as a definite integral.
	www.collegeboard.com /student/testing/ap/calculus_ab/topic.html?calcab (0 words)

	26: Real functions
		Real functions are those studied in calculus classes; the focus here is on their derivatives and integrals, and general inequalities.
		Questions about R^n (say) which are more about the underlying space than about functions on it are dealt with in various geometry and topology pages.
		Convergence of the derivatives of a convergent sequence of functions
	www.math.niu.edu /~rusin/known-math/index/26-XX.html (898 words)

	Jacobian Elliptic Functions
		The References show that elliptic functions appear in familiar works, largely those of handbooks of mathematical functions, but also in Whittaker and Watson where the theory is given in some detail, though the reader may find the presentation difficult.
		Elliptic integrals came first, invented by the Bernoullis, and were studied by Maclaurin, Euler and Lagrange in the 18th century, and later by Legendre, when there was great interest in evaluating the integrals that appeared in scientific applications, after it was realized that most integrals could not be evaluated in terms of the elementary functions.
		The definition of the integral is actually in terms of the definite integral, with its geometric interpretation as the area under the curve y = f(x), while the indefinite integral is a generalization.
	www.du.edu /~jcalvert/math/jacobi.htm (2457 words)

	[No title]
		Maximal functions and integrals of potential type in weighted Lebesgue and Lorentz spaces.
		Weighted norm inequalities for fractional maximal functions and integrals defined on homogeneous type spaces (with J. Genebashvili).
		Criteria for two-weight inequalities for integral transforms with a positive kernel and for maximal functions (with I. Genebashvili and A. Gogatishvili).
	www.rmi.acnet.ge /atestacia/staff/kokil-list.htm (1674 words)

	Lists for mathematics - Eua4xiacwiki
		List of harmonic analysis and representation theory topics
		List of terms relating to algorithms and data structures
		List of it.wp liste di matematici in Italian
	alice.iac.rm.cnr.it:8080 /wiki/index.php/Lists_for_mathematics (131 words)

	Introduction
		A recent table of elliptic integrals [9,10,11,12,13] uses symmetric standard integrals instead of Legendre's integrals because permutation symmetry makes it possible to unify many of the formulas in previous tables.
		Fortran codes for numerical computation of the symmetric integrals, which are homogeneous functions of three or four variables, can be found in several major software libraries as well as in the supplements to [9,10].
		Cases not considered in [16] include two for a completely symmetric integral of the second kind and two for a symmetric integral of the third kind in which two variables are much larger than the other two.
	www.scl.ameslab.gov /Publications/Gus/EllipticIntegrals/node1.html (0 words)

	Functions of one variable
		To find any derivative of the function at any given x, go to Evaluation of function or derivatives and enter the order of the derivative (0 for the function itself, 1 for the first derivative, 2 for the second, etc.) and the point at which you want it evaluated.
		This must be an integer between 1 and 80, and determines the points at which the function or derivative is evaluated when plotting.
		Below is a list of the functions available, including the 8 that have been added.
	www.numericalmathematics.com /functions.htm (1402 words)

	Framingham State College - www.framingham.edu (Site not responding. Last check: )
		After a brief in-depth review of the required algebra and analytical geometry, topics include functions and graphs, polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions.
		A study of functions, limits, continuity, the derivative, rules of differentiation of algebraic and trigonometric functions, applications of differentiation, definite and indefinite integrals, the Fundamental Theorem of Calculus, and applications of integration.
		Vector differential calculus, vector integral calculus including the theorems of Green, Gauss and Stokes, maxima and minima for functions of several variables, Language multipliers, uniform covergence of sequences and series of functions, inverse and implicit function theorems, and Jacobians.
	www.framingham.edu /catalog0304/math_list.htm (0 words)

	Trigonometric Functions (Site not responding. Last check: )
		Trigonometric functions, which comprise one group of transcendental functions, may be differentiated and integrated in the same fashion as the other functions.
		To this point we have considered integrals of trigonometric functions that result in functions of the sine, cosine, and tangent.
		Those integrals that result in functions of the cotangent, secant, and cosecant are included in the following list of elementary integrals:
	www.tpub.com /math2/74.htm (0 words)

	Universiti Tenaga Nasional
		This course introduces functions with three variables, partial derivatives, directional derivatives, extrema for functions with several variables, lagrange multipliers, multiple integrals, cylindrical and spherical coordinates and vector calculus.
		It focused on real numbers, functions, limits, continuity, derivatives, integrals, function of several variables and their applications and finally on vectors.
		Basic probability, continuous and discrete random variables, distribution functions and their applications, relationship between distributions, random sampling, data descriptions, fundamental sampling distributions, single sample estimation and hypotheses testing and simple linear regression and correlation.
	www.uniten.edu.my /newhome/content_list.asp?ContentID=479 (902 words)

	List of integrals of trigonometric functions - Wikipedia, the free encyclopedia
		The following is a list of integrals (antiderivative functions) of trigonometric functions.
		For a complete list of Integral functions, see table of integrals and list of integrals.
		[edit] Integrals of trigonometric functions containing both cos and cot
	en.wikipedia.org /wiki/List_of_integrals_of_trigonometric_functions (0 words)

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