Applications of Integration

Application of Definite Integrals

Toshpo'latova Oydinoy

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.
• A rigorous mathematical definition of the integral was given by Bernhard Riemann.

Definite and Indefinite Integrals

• Integration may be introduced as a means of

finding areas using summation and limits. This

process gives rise to the definite integral of a

function.

• 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 F whose 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.