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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

 

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

 

ANSWER : - (i) The required area is represented by the shaded area ADCBA as

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

  1. The required area is represented by the shaded area ADCBA as

 

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral


Question 2: Sketch the graph of NCERT Solutions Class 12 Maths Chapter 8 - Application of Integraland evaluateNCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

ANSWER : -The given equation is NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

The corresponding values of x and y are given in the following table.

 

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

On plotting these points, we obtain the graph of NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral as follows.

It is known that, NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

Question 3: Find the area bounded by the curve y = sin x between x = 0 and x = 2π

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

 

ANSWER : -The graph of y = sin x can be drawn as

∴ Required area = Area OABO Area BCDB

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral


Question 4: Area bounded by the curve y = x3, the x-axis and the ordinates x = –2 and x = 1 is

A. – 9  
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

 

ANSWER : -

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

Thus, the correct answer is B.

 

Question 5:The area bounded by the curveNCERT Solutions Class 12 Maths Chapter 8 - Application of Integral, 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. 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

ANSWER : -

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

NCERT Solutions Class 12 Maths Chapter 8 - Application of Integral

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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