Differentiation and Integration formula

Calculus can be considered as a branch of mathematics which deals with the study of ‘Rate of Change’ and its implementation in solving equations. 

It is of two major branches: Differential Calculus, which deals with variation, and curve slope, as well as Integral Calculus, which deals with the quantity accumulation along with areas under as well as between curves.

Both branches rely on the fundamental concepts of infinite sequence and infinite series convergence to a very well limit. The fundamental formula of calculus links these two branches together.

The Differential Calculus divides an area into small parts to determine the rate of change. The integral calculus is a process of reasoning or computation that joins minor parts to find the area or volume. This page includes a collection of Calculus Formulas like the integral equation, derivative method, limits formula, and so on.

Because calculus is so important in obtaining the best solution, there are numerous calculus methods involved with the research of the variation of quantities. It uses the derivative of the function to describe the percentage of variation of a function for a given input value.

The process of determining a function’s derivative is known as differentiation. Integration is the inverse process of differentiation. This process assists in maximizing or minimizing the function for just some set, and it frequently represents the various range of options for some particular conditions. The function compares the various options and picks the best optimal answer using various calculus formulas.

Differentiation is the process of determining a function’s derivative. The function’s derivative is described as y = f(x) of the variable x, which would be the variation of variable y concerning variable x change. It denotes a function’s derivative about a variable x. There are several rules for calculating a function’s derivative. These rules simplify the differentiation process for various functions including logarithmic functions, trigonometric functions, and so on. 

The basic function of integration would be to join the slices together to form a whole. Integration is indeed the continuous addition process, and the variable “C” represents the integration constant. However, integration formulas are frequently used to find the most important central points, areas, and volumes. It also aids in determining the area under a curve of the function. Certain integral calculus formulas are useful in obtaining solutions. Such integral calculus methods aid in reducing the time needed to solve.

• . Discover the integral of cos 3x.

Answer:

∫ d/dx(f(x)) =∫ cos 3x

Assume 3x = t

therefore x = t/3

dx = dt/3

The specified integral converts ∫1/3(cos t) dt

= 1/3(sin t) + C

= 1/3 sin (3x) + C

Result: The integral of cos 3x = 1/3 sin (3x) + C