Learning About Integrals – Definition & Application

Mathematics is a very substantial section of any competitive exam whether it is for seeking admission to a famed college for higher studies or employment in a reputable office for an agreeable work profile. The reason behind involving mathematics as a subject is that it helps evaluate a candidate’s problem-solving approach, analytical and logical skills, attention, etc. For some, the subject is not a matter of nervousness or pressure whereas, for some, the subject is a nuisance that they can’t even get rid of unless the purpose is served. Therefore, they keep scratching their heads over the mathematical problems to be able to find the solutions in time and accurately during the exams. Little do they realize, to comprehend mathematical sums and tools one needs to strike the basic concepts. Once the basics are cleared mathematics will no longer be a nuisance while prepping for any competitive exam. 

Usually, the hints to all the problems in mathematics lie in a simple concept that learners fail to understand due to which later they face problems in comprehending and solving mathematical sums. The other reason is a lack of knowledge of mathematical tools or their usage. Through this article, we are going to learn about integrals and their applications. Therefore, make sure that you read the article well and use the knowledge of the application of integrals adequately while solving questions based on them.

What Are Integrals?

• Together with derivatives, integrals are used as a fundamental tool used in calculus.
• It assigns numbers to various functions in such a way that they can describe an area, volume, and displacement, and many other such concepts that can be developed by merging infinitesimal data. 
• In simple terms, an integral can refer to various concepts and it is comparable to summing infinitesimal elements for finding the content of a continuous region. 
• In terms of mathematics, it can be defined as an area or conception of an area. 
• The process of calculating an integral is called integration or quadrature. 
• Moreover, an approximate calculation of integrals is called numerical integration.

What Are The Various Forms Of Integrals?

In calculus, there are basically two forms of integral, the definite integral and the indefinite integrals. Let’s understand them one by one.

Definite Integrals

When there is an integral of a function with definite limits of integration. There are always two limits as the limits of the interval of integration. These limits are known as upper limit and lower limit. Here there are no constants of integration involved to express the intent of vagueness.

Indefinite Integrals 

Now, the indefinite integrals of a function can be defined as the ones with no upper and lower limits of integration. Here, there is a presence of a random constant.

What Are The Most Common Applications Of Integrals?

Integrals are a very useful tool and it finds their application in both science, mathematics, and various professional fields.

• The most familiar application of integrals in mathematics can be seen at the time of calculating areas under a simple curve, parabola, ellipse and lines and arcs of a circle, the center of mass of an object, etc.
• When it comes to science, integrals are used for solving various problems in physics, the most common usages can be seen during calculating the center of gravity, mass, momentum, work done, kinetic energy, velocity, trajectory, thrust, and so on.
• Besides these, integrals are used in architecture for totaling the material usage and construction of layouts, various domains of engineering for computations, in medical sciences for studying the rate of spread of any disease, etc.