Integral Calculus Hand Written Note By Dips Academy

Here, we provided to Integral Calculus Hand Written Note By Dips Academy. Integral Calculus is the branch of calculus where we study about integrals and their properties. Integration is a very important concept which is the inverse process of differentiation. Both the integral calculus and the differential calculus are related to each other by the fundamental theorem of calculus. Free download PDF Integral Calculus Hand Written Note By Dips Academy.

integral calculus hand written note by dips academyIntegral calculus, Branch of calculus concerned with the theory and applications of integrals. While differential calculus focuses on rates of change, such as slopes of tangent lines and velocities, integral calculus deals with total size or value, such as lengths, areas, and volumes. The two branches are connected by the fundamental theorem of calculus, which shows how a definite integral is calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). Free download PDF Integral Calculus Hand Written Note By Dips Academy.

For example, integrating a velocity function yields a distance function, which enables the distance traveled by an object over an interval of time to be calculated. As a result, much of integral calculus deals with the derivation of formulas for finding antiderivatives. The great utility of the subject emanates from its use in solving differential equations. Free download PDF Integral Calculus Hand Written Note By Dips Academy.

Integration Calculus

If we know the f’ of a function which is differentiable in its domain, we can then calculate f. In differential calculus, we used to call f’, the derivative of the function f. Here, in integral calculus, we call f as the anti-derivative or primitive of the function f’. And the process of finding the anti-derivatives is known as anti-differentiation or integration. As the name suggests, it is the inverse of finding differentiation. Integration can be classified into two different categories, namely,

  • Definite Integral
  • Indefinite Integral

1. Definite Integral

An integral that contains the upper and lower limits (i.e) start and end value, then it is known as a definite integral. On a real line, x is restricted to lie. Definite Integral is also called a Riemann Integral when it is restricted to lie on the real line. Free download PDF Integral Calculus Hand Written Note By Dips Academy.

2. Indefinite Integral

Indefinite integrals are not defined using the upper and lower limits. The indefinite integrals represent the family of the given function whose derivatives are f. It returns a function of the independent variable.






Uses of Integral Calculus

Integral Calculus is mainly used for the following two purposes:

  • To calculate f from f’. If a function f is differentiable in the interval of consideration, then f’ is defined in that interval. We have already seen in differential calculus how to calculate derivatives of a function. We can “undo” that with the help of integral calculus.
  • To calculate the area under a curve.

Until now, we have learned that areas are always positive. But as a matter of fact, there is something called a signed area.

Application of Integral Calculus

The important application of integral calculus is as follows. Integration is applied to find:

  • The area between two curves
  • Centre of mass
  • Kinetic energy
  • Surface area
  • Work
  • Distance, velocity, and acceleration
  • The average value of a function
  • Volume
  • Probability


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