Calculus is a very versatile and valuable tool. It is a form of mathematics which was developed from algebra and geometry. It is made up of two interconnected topics:

Calculus is a very versatile and valuable tool. It is a form of mathematics which was developed from algebra and geometry. It is made up of two interconnected topics:

i) Differential calculus

ii) Integral calculus.

Differential calculus is the mathematics of motion and change.

Differential calculus is the mathematics of motion and change.

Integral calculus covers the accumulation of quantities, such as areas under a curve or volumes between two curves.

Integrals and derivatives are the basic tools of calculus, with numerous applications in science and engineering. The two ideas work inversely together in Calculus.

We will discuss about integration and its applications.

INTEGRATION

Integration is an important concept in Mathematics and, together with differentiation, is one of the two main operations in Calculus.

Integration may also be regarded as the reverse of differentiation, so a table of derivatives can be read backwards as a table of anti-derivatives. The final result for an indefinite integral must, however, include an arbitrary constant, because there is a family of curves having same derivatives, i.e. same slope.

Indefinite Integrals

The term Indefinite integral is referred to the notion of antiderivative, a function Fwhose derivative is the given function ƒ. In this case it is called an indefinite integral. Some authors maintain a distinction between anti-derivatives and indefinite integrals.