Candidates can download NCERT Exemplar Class 12 Maths Unit 7 from this page. The exemplar has been provided by the National Council of Educational Research & Training (NCERT) and the candidates can check it from below for free of cost. It contains objective, very short answer type, short answer type, and long answer type questions. Along with it, the answer for each question has also been provided. From the NCERT Exemplar Class 12 Maths Unit 7, candidates can understand the level and type of questions that are asked in the exam.
NCERT Exemplar Class 12 Maths Unit 7 Integrals
NCERT Class 12 Maths Unit 7 is for Integrals. The type of questions that will be asked from NCERT Class 12 Maths Unit 7 are displayed in the below provided NCERT Exemplar Class 12 Maths Unit 7. With the help of it, candidates can prepare well for the examination.
1. Let d/dx F (x) = f (x). Then, we write ∫ f (x) dx = F (x) + C. These integrals are called indefinite integrals or general integrals, C is called a constant of integration. All these integrals differ by a constant.
2. If two functions differ by a constant, they have the same derivative.
3. Geometrically, the statement ∫ f ( x ) dx = F (x) + C = y (say) represents a family of curves. The different values of C correspond to different members of this family and these members can be obtained by shifting any one of the curves parallel to itself. Further, the tangents to the curves at the points of intersection of a line x = a with the curves are parallel.
4. Some properties of indefinite integrals
Methods of integration
There are some methods or techniques for finding the integral where we can not directly select the antiderivative of function f by reducing them into standard forms. Some of these methods are based on
- Integration by substitution
- Integration using partial fractions
- Integration by parts.
The definite integral as the limit of the sum
Fundamental Theorem of Calculus
Some properties of Definite Integrals
Short Answer Type Questions (Solved Examples)
Long Answer Type Questions (Solved Examples)
Objective Type Questions (Solved Examples)
Choose the correct answer from the given four options in each of the Examples from
20 to 30.
Short Answer Type Questions
Long Answer Type Questions
Multiple Choice Questions
Fill In Blanks Type Questions
Click here to download the NCERT Exemplar Class 12 Maths Unit 7 Integrals.