  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 WyzAnt Tutoring

Example:Solve Definite Integral using Properties

 Post to:   Explanation:

Integral A definite integral of a function can be represented as the signed area of the region bounded by its graph.

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

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

(Our solved example in mathguru.com uses the below concept. This is our own explanation, it is not taken from Wikipedia.) = (Property of definite integrals)

Proof : Put a - x = t

-dx = dt

When x = 0, t = a

x = a, t = 0    = LHS