# Xam Idea Class 12 Maths Chapter 9 Solutions: Applications Of The Integrals

Xam Idea 12 Maths Solutions for Chapter 9 ‘Application of Integrals’ is one of the best books for those preparing for exams of senior secondary classes and also preparing for upcoming competitive exams like JEE and NEET. Our Xam Idea Class 12 Maths Solutions help in making your fundamental clear on the chapter. They are completely based on the latest CBSE syllabus along with its examination pattern. The topics covered in these solutions are integrals, types of integrals, how are used for finding the centre of mass of any area with curved sides, finding the area between two curves, finding the area under the curve and the average value of the curve.

Xam Idea 12 Maths Solutions Chapter 9** ‘**Application of Integrals’ consists of a total of 31 questions and has been divided into two categories, long question answers and short answer questions. They are excellently presented in the Xam Idea solutions with a key focus on clearing your concepts. When you practice these problems perfectly, you get a very clear idea of the chapter that will further help in cracking any questions related to this chapter.

The solutions for Xam Idea Class 12 Maths book are prepared by our best subject matter experts in a stepwise manner. Our experts provide the solutions keeping in mind your level of understanding. They also provide all tricks and tips necessary for attempting any question related to this chapter. Our Xam Idea solutions provide help to both the learners as well as teachers.

## Important Topics of Xam Idea Class 12 Maths Solutions Chapter 9: Application of Integrals

The chapter possesses an immense vitality for students appearing for the exam of senior secondary exams. Attempting long term questions needs a lot of description in the solution, thereby clearing all doubts among students.

- An integral is a kind of function of which the given function is a derivative. It is utilized for obtaining the areas of two-dimensional regions and calculating the volumes of three-dimensional objects. Thus, when you find the integral of a function in respect to X, it implies finding the area to the X-axis from the curve. The integral is also known as anti-derivative as it is the reverse process of differentiation.
- Two types of integrals are definite integral and indefinite integral. The definite integral is an integral with definite limits and also called Rieman integral. It is represented in the form of ∫ba f(x)d(x).
- An indefinite integral is something whose upper and lower limits are not defined as ∫f(x)d(x)=F(x)+C, is defined as the indefinite integral, where C is the constant value.
- Integrals are used for finding the centre of mass of any area with curved sides, finding the area between two curves, finding the area under the curve and the average value of the curve.
- The area of any region surrounded by the curve Y=f(x), X-axis and the lines X= and X=b where b>a is given by the formula ba YDX= ba f(x)d(x).
- The area of the region bounded by the curve x= θ(Y), Y-axis and the lines y=c and y=d, is given by the formula area = c d xdy= c dy dy
- When area of the region is enclosed by two curves y=f(x) and y= g(x), and the line x=a and x=b, then is given by the formula Area = f(x) – g(x) dx where f(x) g(x) in [a,b].

### Exercise Discussion of Xam Idea Class 12 Maths Solutions Chapter 9: Application of Integrals

- Chapter 9 Application of Integrals of Xam Idea Class 12 Maths Solutions consist of about 34 long questions.
- The first 29 questions are quite tricky long questions based on finding the area of the region bounded by lines, area of the region between parabolas, area of the region between two circles, area of the part of the circle exterior to the parabola.
- You have to be extremely careful while using formulas for solving those questions.
- The next 5 questions are very lengthy and involve reasoning based questions. Based on the area of the region, the value of the graph etc. Properly solving these questions will offer you the required assistance for cracking exams easily.

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