# Applications of Definite Integration | Area | Volume

By learning objective of definite integration, students will be able to compute area between two curves with respect to an axis and y axis. Also using application of DI we able to solve Area under the curve and Volume of revolution. ## MajorLearningOutcomes:

• Solve given simple problems based on properties of D.I.
• Apply the concept of D.I. to find the area under the given curve(s).
• Utilize the concept of D.I. to find area between given two curves.
• Invoke the concept of D.I. to find the volume of revolution of given surface.

## Definite Integration

The definite integration is defined as exactly the limit and summation that we looked at in the last section of equation. To find the net area between a function and the axis which is given. Also the notation for the definite integral is nearly similar to the notation for an indefinite integral but difference is that D.I. has limit. One is upper limit and other one is lower limit.

Topics and Sub-topics of D.I. is given below:

a) Definite Integration:

• Simple examples
• Properties of definite integral (without proof) and simple examples.

b) Applications of definite integration:

Area under the curve.

Some examples of area under the curve are given below.

1. Obtain the area between line y = 8x, X-axis and ordinates at x = 2 and x = 6.
2. Find the area bounded by y = 4x –x2 meeting the X-axis and the ordinate x = 1, x = 3.
3. By using method of integration find the area of circle x2 + y2 = a2 .
4. Using integration find area of ellipse x2 / a2 + y2 / b2 = 1

Area between two curves.

Some examples of area between two curves are given below.

1. Find the area between the parabola y = x2 and the line y = 4.
2. Area of region included between the parabola y = x2 + 1 and a line y= 2x + 1.

Volume of revolution.