• Pallavi Saikia

Calculus is a branch of Mathematics which is associated with the calculation of instantaneous rates of variation, the fundamental principle of the sub-branch of Calculus i.e., Differential Calculus and the addition of infinitely many infinitesimal elements or partitions to calculate the entire as a whole is the basic functioning principle of the other sub-branch of Calculus i.e., the Integral Calculus which is the topic of study of this paper. Integral calculus is that sub-branch of Calculus apportioning with the concepts and applications of different integrals in different practical scenarios. Out of the two emerging vital sub-branches of Mathematics, Differential Calculus emphasizes on the point at which frequency, a change or variation occurs at an instantaneous time. For instance, in calculating the gradients of tangent lines and velocities. Integral Calculus deals with areas and volumes. These two twigs are coupled by the fundamental theorem of Calculus that illustrates the procedure in which manner, a definite integral is calculated by dint of its antiderivative. During the 17th century, two significant figures in the field of mathematicians, one from England and the other from Germany, viz., Sir Isaac Newton and Gottfried Wilhelm Leibniz respectively, should be intensely honoured for simultaneously making research but not knowingly one another on the most applicable significant sub-branch of Mathematics across the world i.e., Calculus. Calculus is now emanating as the key subject to be learnt by the scholars, practicing in the fields of Mathematics, Physics, Economics, Commerce and Finance. Calculus turns it conceivable to resolve the complications arising in solving the analytical criticalities in the research arenas of Mathematics, Physics and Econometrics. With the advancements of the modern digitalized technologies and with the strenuous innovations of the artificial intelligences, computers are put forwarding an energetic bridge between finding solutions arising in the fields of calculus complications and intricate concepts that were previously pondered dreadfully problematic. The extraordinary effectiveness of the sub-branch springs from its practice in solving differential equations and calculus of variations.

Calculus, infinitesimal, limit, continuity, derivative.

"The Embedded Mathematics Behind Integral Calculus", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 8, page no.g284-g294, August-2023, Available :http://www.jetir.org/papers/JETIR2308631.pdf

"The Embedded Mathematics Behind Integral Calculus", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 8, page no. ppg284-g294, August-2023, Available at : http://www.jetir.org/papers/JETIR2308631.pdf