The definite integration technique has numerous applications in various fields, such as physics, engineering, economics, and statistics. The Class 12 Mathematics syllabus covers the following topics related to the application of definite integration:
Area Between Two Curves: This topic covers the application of definite integration in finding the area enclosed between two curves.
Applications of Definite Integrals: This topic covers the applications of definite integrals in finding the volume of solids of revolution, finding the length of a curve, finding the center of mass of a solid, and solving problems related to work, force, and energy.
Differential Equations: This topic covers the application of definite integration in solving differential equations using the method of separation of variables.
Probability: This topic covers the application of definite integration in calculating probabilities and finding the mean and variance of a probability distribution.
The applications of definite integration are important because they provide a powerful tool for solving problems related to areas, volumes, and forces. The technique of finding the area between two curves is used in solving problems related to optimization, related rates, and curve sketching. The applications of definite integrals in finding the volume of solids of revolution and finding the length of a curve are used in physics and engineering. The application of definite integration in solving differential equations is used in various fields such as physics, chemistry, and engineering. The application of definite integration in calculating probabilities and finding the mean and variance of a probability distribution is used in statistics and economics.