JEE Exam  >  JEE Notes  >  Mathematics (Maths) for JEE Main & Advanced  >  NCERT Solutions - Exercise 8.1 : Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

Application of Integral

Question 1: Find the area of the region bounded by the ellipse NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

ANSWER : - The given equation of the ellipse, NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral, can be represented as

It can be observed that the ellipse is symmetrical about x-axis and y-axis.

 

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

∴ Area bounded by ellipse = 4 × Area of OAB

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

Therefore, area bounded by the ellipse = 4 × 3π = 12π units

Question 2: Find the area of the region bounded by the ellipse NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

ANSWER : -The given equation of the ellipse can be represented as

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

It can be observed that the ellipse is symmetrical about x-axis and y-axis.

∴ Area bounded by ellipse = 4 × Area OAB

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

Therefore, area bounded by the ellipse = NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

 


 Question 3: Area lying in the first quadrant and bounded by the circle x2  +  y2 = 4 and the lines x = 0 and x = 2 is

A. π  

B. NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral 

C. NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral 

D. NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

 

ANSWER : -The area bounded by the circle and the lines, x = 0 and x = 2, in the first quadrant is represented as

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

Thus, the correct answer is A.

 Question 4: Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is

A.

B. NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

C. NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

D. NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

 

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

ANSWER : - The area bounded by the curve, y2 = 4x, y-axis, and y = 3 is represented as

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

Thus, the correct answer is B.

The document NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral is a part of the JEE Course Mathematics (Maths) for JEE Main & Advanced.
All you need of JEE at this link: JEE
210 videos|446 docs|143 tests

Up next

FAQs on NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

1. What is the application of integrals?
Ans. The application of integrals involves finding areas, volumes, and other quantities by using the concept of integration. It is used in various fields such as physics, engineering, economics, and statistics to solve problems related to accumulation, rate of change, and optimization.
2. How do integrals help in finding areas?
Ans. Integrals help in finding areas by dividing the region into small rectangles or trapezoids, calculating the area of each small portion, and then adding them up using the concept of integration. This method is called the definite integral and is denoted by the symbol ∫.
3. Can integrals be used to determine the volume of irregular shapes?
Ans. Yes, integrals can be used to determine the volume of irregular shapes. By applying the concept of integration to three-dimensional figures, we can calculate the volume of irregular shapes such as cones, spheres, and pyramids.
4. What are the real-life applications of integrals?
Ans. Integrals have numerous real-life applications. They are used in physics to calculate the work done by a force, in economics to determine the total revenue and cost functions, in biology to model population growth, and in statistics to find the probability distribution functions.
5. How are integrals used in optimization problems?
Ans. Integrals are used in optimization problems to find the maximum or minimum value of a function. By setting up an appropriate equation and using the techniques of calculus, we can solve optimization problems to determine the optimal solution for various scenarios, such as maximizing profit or minimizing cost.
210 videos|446 docs|143 tests
Download as PDF

Up next

Explore Courses for JEE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

ppt

,

Sample Paper

,

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

,

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

,

video lectures

,

Objective type Questions

,

Previous Year Questions with Solutions

,

Semester Notes

,

Exam

,

pdf

,

Summary

,

past year papers

,

Important questions

,

practice quizzes

,

Free

,

mock tests for examination

,

study material

,

Viva Questions

,

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

,

Extra Questions

,

shortcuts and tricks

,

MCQs

;