Mathematics is a subject that has a wide range of applications in our daily lives, from calculating the amount of change we should receive from a purchase to analyzing data in a scientific study. In Class 12, the students learn about calculus, which is a branch of mathematics that studies the change in a function over time. Chapter 8 of the NCERT Solutions Class 12 Maths textbook deals with Applications of Integrals.
In this chapter, the students will learn how to use integration to solve problems related to finding the area under curves, volumes, and lengths of curves. This chapter also covers the application of integrals in physics, such as calculating the work done by a force, and in economics, such as calculating the consumer surplus.
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This chapter contains six main topics, each with several subtopics that cover different aspects of applications of integrals. The first topic is about the area under a curve, where the students learn how to calculate the area under a curve using integration. The second topic is about the area between two curves, where the students learn how to find the area between two curves using integration. The third topic is about the volume of a solid, where the students learn how to calculate the volume of a solid using integration.
The fourth topic is about the length of a curve, where the students learn how to find the length of a curve using integration. The fifth topic is about the work done by a force, where the students learn how to calculate the work done by a force using integration. The final topic is about the application of integrals in economics, where the students learn how to calculate the consumer surplus using integration.
NCERT Solutions Class 12 Maths Chapter 8 is an essential part of the Class 12 Maths syllabus, and the students who have a strong foundation in this chapter will find it easier to understand and solve problems in the future. By understanding the applications of integrals, the students will be able to solve problems in various fields, such as physics, economics, and engineering.
NCERT Solutions Class 12 Maths Chapter 8 provides step-by-step solutions to all the problems in the textbook, making it easier for the students to understand the concepts and solve the problems. By practicing the problems in this chapter, the students will be able to improve their problem-solving skills and become more confident in their ability to solve complex problems.
Area under a Curve: The first topic of this chapter covers the concept of finding the area under a curve. The students will learn how to calculate the area between the x-axis and a curve using integration. This concept is crucial in understanding the properties of curves and finding the area of irregular shapes.
Area between Two Curves: The second topic of this chapter teaches students how to calculate the area between two curves using integration. This concept is widely used in physics and engineering to determine the area of complex shapes and solve various real-life problems.
Volume of a Solid: The third topic of this chapter deals with the calculation of the volume of a solid using integration. The students will learn how to use the definite integral to find the volume of a solid obtained by rotating a curve around an axis. This concept is used extensively in engineering and physics to calculate the volume of complex shapes.
Length of a Curve: The fourth topic of this chapter covers the concept of finding the length of a curve using integration. The students will learn how to calculate the length of a curve by dividing it into small segments and then integrating the lengths of each segment. This concept is essential in the study of geometry and calculus and is used in various fields such as engineering, physics, and architecture.
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NCERT Solutions Class 12 Maths Chapter 8: Applications of Integrals is an essential chapter in the Class 12 Maths syllabus. By understanding the concepts in this chapter, the students will be able to solve problems in various fields, such as physics, economics, and engineering. NCERT Solutions provided by Oswaal Books make it easier for the students to understand the concepts and solve the problems. By practicing the problems in this chapter, the students will be able to improve their problem-solving skills and become more confident in their ability to solve complex problems.
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