table of integrals - Article Index

Encyclopedia - Antiderivative: Encyclopedia - Antiderivative
In calculus, an antiderivative or primitive function of a given real valued function f is a function F whose derivative is equal to f, i....   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia - Trigonometric Function
In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena....   » Read the article

Encyclopedia - Antiderivative: Encyclopedia Ii - Antiderivative - Uses And Properties
Antiderivatives are important because they can be used to compute integrals, using the fundamental theorem of calculus: if F is an antide...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - History
The earliest systematic study of trigonometric functions and tabulation of their values was performed by Hipparchus of Nicaea (180-125 BC...   » Read the article

Encyclopedia - List Of Integrals Of Irrational Functions: Encyclopedia Ii - List Of Integrals Of Irrational Functions - Integrals Involving
Assume (x2 > a2), for (x2 < a2), see next section: Note that , where the positive value of is to be taken. ...   » Read the article

Encyclopedia - Mercator Projection: Encyclopedia Ii - Mercator Projection - Controversy
Like all map projections, attempting to fit a curved surface onto a flat sheet, the shape of the map is a distortion of the true layout o...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - History
The earliest systematic study of trigonometric functions and tabulation of their values was performed by Hipparchus of Nicaea (180-125 BC...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Series Definitions
Please note: Here, and generally in calculus, all angles are measured in radians. (See also below). Using only geometry and properties of...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Unit-circle Definitions
The six trigonometric functions can also be defined in terms of the unit circle, the circle of radius one centered at the origin. The uni...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Right Triangle Definitions
In order to define the trigonometric functions for the angle A, start with an arbitrary right triangle that contains the angle A: We use ...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Definitions Via Differential Equations
Both the sine and cosine functions satisfy the differential equation i.e. each is the additive inverse of its own second derivative. W...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Other Definitions
Theorem: There exists exactly one pair of real functions s, c with the following properties: For any : ... See also:Trigono...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Properties And Applications
The trigonometric functions, as the name suggests, are of crucial importance in trigonometry, mainly because of the following two results...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Inverse Functions
The trigonometric functions are periodic, so we must restrict their domains before we are able to define a unique inverse. In the followi...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Computation
The computation of trigonometric functions is a complicated subject, which can today be avoided by most people because of the widespread ...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - List Of Trigonometric Functions
A few other functions were common historically (and appeared in the earliest tables), but are now little-used, such as: versed sine (ver...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Definitions Via Differential Equations
Both the sine and cosine functions satisfy the differential equation i.e. each is the additive inverse of its own second derivative. W...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Properties And Applications
The trigonometric functions, as the name suggests, are of crucial importance in trigonometry, mainly because of the following two results...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Inverse Functions
The trigonometric functions are periodic, so we must restrict their domains before we are able to define a unique inverse. In the followi...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Computation
The computation of trigonometric functions is a complicated subject, which can today be avoided by most people because of the widespread ...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Series Definitions
Please note: Here, and generally in calculus, all angles are measured in radians. (See also below). Using only geometry and properties of...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Unit-circle Definitions
The six trigonometric functions can also be defined in terms of the unit circle, the circle of radius one centered at the origin. The uni...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Right Triangle Definitions
In order to define the trigonometric functions for the angle A, start with an arbitrary right triangle that contains the angle A: We use ...   » Read the article

Encyclopedia - Mercator Projection: Encyclopedia Ii - Mercator Projection - Derivation Of The Projection
Assume a spherical Earth. (It is actually slightly flattened, but for small-scale maps the difference is immaterial. For more precision, ...   » Read the article

Encyclopedia - Trigonometric Function: Encyclopedia Ii - Trigonometric Function - Other Definitions
Theorem: There exists exactly one pair of real functions s, c with the following properties: For any : ... See also:Trigono...   » Read the article