JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > 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 
ANSWER : - The given equation of the ellipse, 
, can be represented as
It can be observed that the ellipse is symmetrical about x-axis and y-axis.
∴ Area bounded by ellipse = 4 × Area of OAB
Therefore, area bounded by the ellipse = 4 × 3π = 12π units
Question 2: Find the area of the region bounded by the ellipse 
ANSWER : -The given equation of the ellipse can be represented as
It can be observed that the ellipse is symmetrical about x-axis and y-axis.
∴ Area bounded by ellipse = 4 × Area OAB
Therefore, area bounded by the ellipse = 
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. 
C. 
D. 
ANSWER : -The area bounded by the circle and the lines, x = 0 and x = 2, in the first quadrant is represented as
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. 2
B. 
C. 
D. 
ANSWER : - The area bounded by the curve, y2 = 4x, y-axis, and y = 3 is represented as
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) Class 12.
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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.
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