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Application of Integrals 12th Notes - Free NCERT Class 12 Maths Chapter 8 Notes - Download PDF

Application of Integrals 12th Notes - Free NCERT Class 12 Maths Chapter 8 Notes - Download PDF

Edited By Ramraj Saini | Updated on Apr 23, 2022 12:48 PM IST

Introduction: Class 12 Math chapter 8 notes are regarding Applications of integrals. In chapter 7 integrals we already learned about integrations, now in Applications of integrals Class 12 notes contain about finding the area of the functions and curves that is nothing but finding the total area of the curve. This Class 12 Maths chapter 8 notes contains the following topics: area under a single curve, area under two curves, area of the region bounded by a curve, and a line. NCERT Class 12 Math chapter 8 notes also contain standard formulas that are to be remembered for the implementation in problems.

This Story also Contains
  1. NCERT Class 12 Chapter 8 Notes
  2. Significance of NCERT Class 12 Maths Chapter 8 Notes:
  3. NCERT Books and Syllabus

NCERT Class 12 Math chapter 8 contains a detailed explanation of topics, examples, exercises. By going through the document students can cover all the topics that are in NCERT Notes for Class 12 Math chapter 8 textbook. It also contains examples, exercises, a few interesting points and most importantly contains FAQs that are frequently asked questions by students which can clarify many other students with the same doubt. Every concept that is in CBSE Class 12 Maths chapter 8 notes is explained here in a simple and understanding way that can reach students easily. All these concepts can be downloaded from Class 12 Maths chapter 8 notes pdf download, Class 12 notes Applications of integrals, Applications of integrals Class 12 notes pdf download.

Also, students can refer,

NCERT Class 12 Chapter 8 Notes

Application of integrals is about integrating and finding areas under curves. Integrating is adding or summation of all the points.

General equation of area under curves:

y=f(x)

Area under simple curves:

Area under the curve is y=f(x) with coordinates x=a, x=b.

Graph for Area Under Curves:

According to class 12 Applications of integrals notes, graph for area under curves is:

1645012679810

Now finding the integral of the function:

Step1: Write down the equation

A=y=f(x)

Here A denotes area

Step2: Take integration on both sides.

\int_{a}^{b} A= \int_{a}^{b}y dx= \int_{a}^{b} f(x) dx

Step3: Find the integration

Step4: Apply the limits and solve the equation.

Similarly, if it is for x terms then equation is:

x=g(y) with coordinates y=a, y=b.

Area of the above equation:

\int_{a}^{b} A= \int_{a}^{b} xdy= \int_{a}^{b} g(y) dy

Meanwhile, when we get an area as positive after solving the equation then we have no issues.

But if we get area negative then as the area doesn’t exist in negative value so we take their absolute value that is nothing but,

\left | \int_{a}^{b} f(x) dx\right |

Finding the area of the region bounded by a curve and a line:

It is the same as finding an area under the curves.

But the only difference is we find the area of the region that is only enclosed by a line and a circle.

Graph for Curve Bounded by Line:

1645012723407

Area between two curves:

Here we have two curves:

a) y=f(x)

b) y=g(x), where f(x)>g(x) in the interval [a, b].

FORMULAS FOR AREA UNDER TWO CURVES:

if y=f(x) and y=g(x)

a) when f(x)>g(x) in interval [a, b]

A= \int_{a}^{b} \left (f(x)-g(x) \right ) dx

b) when f(x) > g(x) in [a, c] and f(x) < g(x) in [c, b]

A= \int_{a}^{c} \left (f(x)-g(x) \right ) dx +\int_{c}^{b} \left (g(x)-f(x) \right ) dx

Graph Between Two Curves:

In NCERT notes for Class 12 Maths chapter 8, the graph between two curves is given as:

1645012754737


With this topic we conclude NCERT Class 12 chapter 8 notes.

The link for the NCERT textbook pdf is given below:

URL: ncert.nic.in/ncerts/l/lemh202.pdf

Significance of NCERT Class 12 Maths Chapter 8 Notes:

NCERT Class 12 Maths chapter 8 notes will be very much helpful for students to score maximum marks in their 12 board exams. In Applications of integrals Class 12 chapter 8 notes, we have discussed many topics: area under single curve, area under two curves, area of the region bounded by a curve, and a line like with their mathematical representations, along with the graphs. NCERT Class 12 MMathematics chapter 8 is also very useful to cover major topics of the Class 12 CBSE Mathematics Syllabus.

The CBSE Class 12 Maths chapter 8 will help to understand the formulas, statements, rules with their conditions in detail. This pdf also contains previous year’s questions and NCERT TextBook pdf. The next part contains FAQ’s most frequently asked questions along with topic-wise explanations. By referring to the document you can get a complete idea of all the topics of Class12 chapter 8 Applications of integrals pdf download.

NCERT Class 12 Notes Chapter Wise.


Go through the above link to learn more examples topic-wise.

Subject Wise NCERT Exampler Solutions

Subject Wise NCERT Solutions

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NCERT Books and Syllabus

NCERT Book for Class 12
NCERT Syllabus for Class 12


Frequently Asked Question (FAQs)

1. What is the role of Applications of integrals Class 12 notes?

They are used to calculate the area of the curves, combine or integrate functions, and many more.

2. Difference between integration and differentiation in Class 12 Math chapter 8 notes?

Integration is just the reverse of differentiation.

Differentiation calculates the slope whereas integration calculates the area under the curve.

3. What is the use of Class 12 notes Applications of integrals in our daily life?

To calculate area, cost, maximum and minimum values, amount of material needed, profit, and loss.

4. What is the meaning of calculus?

It is generally a study on shapes, algebra using arithmetic operations. It is classified into two branches: Differential and integral calculus. Differentiations, integrations, limits all come under this.

5. How many types of techniques do we have in Class 12 Maths chapter 8 notes?

Integration by dividing into parts, substitution, reverse chain rule, solving trigonometric equations, etc…..

These solutions can be obtained from Class 12 Maths chapter 8 notes pdf download.

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