NCERT Exemplar Class 12 Maths Chapter 8 Solutions: Application of Integrals
NCERT Exemplar Class 12 Maths Solutions Chapter 8 will help you to understand various integral applications in the easiest possible way so that you can score good marks in exams. This NCERT Exemplar Class 12 Maths has been assembled together, that helps you to get clear with all the concepts, different formulas as well as mathematical questions precisely.
In this chapter, there are 34 Exemplar problems divided into 4 exercises related to Area under simple curves, the area between lines and arcs of circles, parabolas, and ellipses. NCERT Exemplar Class 12 Maths problems with solutions will also help you to understand the various integral applications, different properties of definite and indefinite integrals along with their applications, cutoff points of integration, indefinite integral applications, and the area of the region bounded by the curve or enclosed between two curves.
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Important Topics NCERT Exemplar Class 12 Maths Solutions Chapter 8 – Application of Integrals
There are various strategies for calculations among which are differentiation, functions as well as integration. The use of Integrals is applied in different fields like Mathematics, Science, Engineering, and so forth. For the estimation of areas, we use significant integral equations.
- Area covered by simple curve:
In this section, you will get to know about the enclosed area by the curve by Leibnitz Rule, assessment and properties of definite integrals by substitution, integral functional properties, definition, and properties of the gamma function and Walli’s formula.
The area within bounded region by the curve were, y = f (x), x-axis and the lines x = a and x = b (b > a) is denoted by the formula:
- The area within the bounded region of a curve and a line:
Here, you will get to know about various areas of a part bounded through a line and a circle, a line, and a parabola, a line, and an ellipse. The area of the bounded region by a curve was, x = Φ (y), y-axis and the lines y = c, y = d is given by the formula:
The area of the region confined between two curves was, y = f (x), y = g (x) and the lines x = a, x = b is given by the formula.
- The area between two curves
This part of the exemplar problems in NCERT Exemplar for class 12 maths chapter 8 tells you about the area confined within two curves, area of curves given by polar equations, area of parametric curves.
Exercise Discussion of NCERT Exemplar Class 12 Maths Solutions Chapter 8 – Application of Integrals
The total number of exemplar problems in chapter 8 of NCERT Exemplar book of class 12 include short answers type questions, long answers questions, and objective type questions.
- The first exercise includes 15 short answers type exemplar questions and 2 MCQs based on the formulas of the area covered by simple curve, the area within the bounded region of a curve and a line and area between two curves.
- The second exercise includes 7 questions in total (5 long questions, 2 MCQs) asking you to solve problems by using the formula for an area in between two curves.
- The third exercise includes 19 miscellaneous questions and examples based upon various applications of integral.
Such high-level problems mentioned in CBSE Class 12 Exemplar Maths Chapter 8 helps you to develop your skills of problem-solving that boost your confidence towards the chapter and help you to solve even critical questions smoothly in your CBSE exams.
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