If you like what you see in Mathguru
Subscribe Today
 For 12 Months US Dollars 12 / Indian Rupees 600 Available in 20 more currencies if you pay with PayPal. Buy Now No questions asked full moneyback guarantee within 7 days of purchase, in case of Visa and Mastercard payment

Example:Evaluate integral of Trigonometric Function

 Post to:

Explanation:

Integral

Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. Given a function ƒ of a real variable x and an interval [ab] of the real line, the definite integral

is defined informally to be the net signed area of the region in the xy-plane bounded by the graph of ƒ, the x-axis, and the vertical lines x = a and x = b.

The term integral may also refer to the notion of antiderivative, a function F whose derivative is the given function ƒ. In this case, it is called an indefinite integral and is written:

The integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between antiderivatives and indefinite integrals.

The principles of integration were formulated independently by Isaac Newton and Gottfried Leibniz in the late 17th century. Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if ƒ is a continuous real-valued function defined on a closed interval [ab], then, once an antiderivative F of ƒ is known, the definite integral of ƒ over that interval is given by

http://en.wikipedia.org/wiki/Integral

Integrals of simple functions

C is used for an arbitrary constant of integration that can only be determined if something about the value of the integral at some point is known. Thus each function has an infinite number of antiderivatives.

### Trigonometric functions

more integrals: List of integrals of trigonometric functions

(See Integral of the secant function. This result was a well-known conjecture in the 17th century.)

(Our solved example in mathguru.com uses this concept)

(see integral of secant cubed)

http://en.wikipedia.org/wiki/Lists_of_integrals