JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > NCERT Solutions - Exercise Miscellaneous : Application of Integral
NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral
Question 1: Find the area under the given curves and given lines:
(i) y = x2, x = 1, x = 2 and x-axis
(ii) y = x4, x = 1, x = 5 and x –axis
ANSWER : - (i) The required area is represented by the shaded area ADCBA as
- The required area is represented by the shaded area ADCBA as
Question 2: Sketch the graph of 
and evaluate
ANSWER : -The given equation is 
The corresponding values of x and y are given in the following table.
On plotting these points, we obtain the graph of 
as follows.
It is known that, 
Question 3: Find the area bounded by the curve y = sin x between x = 0 and x = 2π
ANSWER : -The graph of y = sin x can be drawn as
∴ Required area = Area OABO Area BCDB
Question 4: Area bounded by the curve y = x3, the x-axis and the ordinates x = –2 and x = 1 is
A. – 9
B. 
C. 
D. 
ANSWER : -
Thus, the correct answer is B.
Question 5:The area bounded by the curve
, x-axis and the ordinates x = –1 & x = 1 is given by [Hint: y = x2 if x > 0 and y = –x2 if x < 0]
A. 0
B. 
C. 
D. 
ANSWER : -
Thus, the correct answer is C.
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 are the different applications of integrals? |  |
Ans. Integrals have various applications in real-life scenarios. Some common applications include finding areas and volumes, calculating work done, determining the center of mass, analyzing population growth, and solving differential equations.
| 2. How can integrals be used to find areas and volumes? | |
Ans. Integrals can be used to find the area under a curve, which represents the area between the curve and the x-axis. Similarly, integrals can also be used to find the volume of a solid obtained by rotating a curve around an axis, using the method of disks or washers.
| 3. What is the significance of integrals in calculating work done? | |
Ans. Integrals are used to calculate work done in physics. By integrating a force function over a given displacement, the integral gives the work done by the force. This is particularly useful in situations where the force varies along the path.
| 4. How can integrals be applied to determine the center of mass? | |
Ans. Integrals are used to calculate the center of mass of an object. By considering the mass distribution and integrating over the object's volume or area, the integral gives the coordinates of the center of mass.
| 5. Can integrals be used to solve differential equations? | |
Ans. Yes, integrals play a crucial role in solving differential equations. By integrating both sides of a differential equation, it is possible to obtain a general solution. Integrating further with appropriate initial or boundary conditions can yield specific solutions.
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