In NCERT Class 12 Mathematics Chapter 8, titled Application of Integrals, students explore how integrals can be applied to solve real-world problems. This chapter focuses on finding areas enclosed by curves, volumes of solids of revolution, and other practical applications of definite integrals. Students learn to analyze geometrical problems and apply integral calculus techniques to compute areas under curves, between curves, and in bounded regions.
This article provides a comprehensive guide to mastering the Application of Integrals. It includes sample MCQs and subjective questions for CBSE and CUET, along with downloadable PDFs for Class 12 Mathematics Chapter 8 MCQs and previous year questions to aid exam preparation.
|
NCERT Class 12 Mathematics Chapters
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Class 12 Mathematics Chapter 8 MCQs
This question bank includes previous years' CUET and CBSE MCQs, along with questions curated by subject experts. Below are 5 sample MCQs for Class 12 Mathematics Chapter 8: Application of Integrals. For the full set of 50 MCQs, download the PDF using the link provided below.
|
1.
|
Area of the region bounded by the curve x2 = 4y, x -axis and x = 3 is:
(a) sq. units (b) sq. units (c) sq. units (d) sq. units |
|
2.
|
The area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 is:
(a) sq. units (b) sq. units (c) sq. units (d) sq. units |
|
3.
|
The area of region bounded by the curve y = cos x and x-axis between x = 0 and x = π is
(a) 1 sq. unit (b) 2 sq. units (c) 3 sq. units (d) 4 sq. units
|
|
4.
|
Area bounded by and its latus rectum is: (a) sq. units (b) sq. units (c) sq. units (d) 2 sq. units |
|
5.
|
The area of the region bounded by the parabola y2 = 4ax and its latus rectum is:
(a) sq. units (b) sq. units (c) sq. units (d) sq. units |
CUET Free Master Classes:
Class 12 Mathematics Chapter 8 Subjective Questions Without Solutions
This section provides previous years' CBSE subjective questions (2 marks and above), along with expert-curated questions. Below are 5 sample subjective questions for Class 12 Mathematics Chapter 8: Application of Integrals. For the complete set, download the PDF using the link below.
|
1.
|
Sketch the region bounded by the lines 2x + y = 8, y = 2, y = 4 and the y-axis. Hence, obtain its area using integration.
(CBSE 2023, 2M)
|
|
2.
|
Find the area of the minor segment of the circle x2 + y2 = 4 cut off by the line x = 1, using integration.
(CBSE 2023, 3M)
|
|
3.
|
Using integration, find the area of the region bounded by y = mx (m > 0), x = 1, x = 2 and the x-axis.
(CBSE 2023, 3M)
|
|
4.
|
Find the area of the region {(x, y) : x2 ≤ y ≤ x + 2}, using integration.
(CBSE 2022, 3M)
|
|
5.
|
Using integration, find the area of the region {(x, y) : y2 ≤ x ≤ y}.
(CBSE 2022, 3M)
|
Class 12 Mathematics Chapter 8 Sub Topics
|
Chapter Name
|
Sub Topic Name
|
|
Application of Integrals
|
8.1 Introduction to Applications of Integrals
|
|
8.2 Finding Areas Bounded by Curves
|
|
8.3 Area Between Two Curves
|
|
8.4 Solids of Revolution and Volumes
|
|
8.5 Real-World Applications of Definite Integrals
|
Review of NCERT Class 12 Mathematics Chapter 8
NCERT Class 12 Mathematics Chapter 8,
Application of Integrals, provides students with a practical understanding of integral calculus and its applications in solving geometrical problems. The chapter covers techniques for finding areas of regions enclosed by curves and calculating volumes of solids of revolution. These concepts are essential for students preparing for
CBSE,
CUET, and other competitive exams. Mastery of this chapter equips students with the tools to analyze and solve real-world problems using integral calculus.