# Application of Integrals: Integrals Used to Find the Area of a Curved Region (For CBSE, ICSE, IAS, NET, NRA 2022)

Doorsteptutor material for CBSE/Class-12 is prepared by world's top subject experts: get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-12.

## Application of Integrals

• There are several methods of calculations among which are functions, differentiation, and integration.
• Application of Integrals is applied in various fields like Mathematics, Science, and Engineering etc.
• An integral is a function, of which a given function is the derivative. Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects.
• For the calculation of areas, we use majorly integrals formulas.

## Integrals Used to Find the Area of a Curved Region

• There are basically two types of integrals, Definite and Indefinite. Definite Integral is defined as the integral which contains definite limits, i.e.. , upper limit and lower limit. It is also named as Riemann Integral. It is represented as-
• Indefinite Integral is defined as the integral whose upper and lower limits are not defined.
• , is defined as the indefinite integral, where C is the constant value.

## Application of Integrals

• There are many applications of integrals, out of which some are mentioned below:

### In Physics

• Integrals are used to calculate
• Centre of gravity
• Mass and momentum of inertia of vehicles
• Mass and momentum of satellites
• Mass and momentum of a tower
• The centre of mass
• The velocity of a satellite at the time of placing it in orbit
• The trajectory of a satellite at the time of placing it in orbit
• To calculate Thrust

### In Maths

• To find the centre of mass (Centroid) of an area having curved sides
• To find the area between two curves
• To find the area under a curve
• The average value of a curve

Developed by: