NCERT Exemplar Class 12 Maths Chapter 7: Integrals. NCERT Exemplar Solutions for Class 12 Maths Chapter 7 Integrals prepare students for their Class 12 exams thoroughly.

Maths problems and solutions for the Class 12 pdf are provided here which are similar to the questions being asked in the previous year’s board.

**NCERT Exemplar Class 12 Maths Chapter 7: Integrals**

Class 12: Maths Chapter 7 solutions. Complete Class 12 Maths Chapter 7 Notes.

**Overview**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.

**Definite integral**

**The definite integral as the limit of the sum**

Click here to download the NCERT Exemplar Class 12 Maths Unit 7 Integrals.

**Fundamental Theorem of Calculus**

**Some properties of Definite Integrals**

### Short Answer Type Questions (Solved Examples)

Click here to download the NCERT Exemplar Class 12 Maths Unit 7 Integrals.

### 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

Click here to download the NCERT Exemplar Class 12 Maths Unit 7 Integrals.

### Long Answer Type Questions

### Multiple Choice Questions

Click here to download the NCERT Exemplar Class 12 Maths Unit 7 Integrals.

### Fill In Blanks Type Questions

Click here to download the NCERT Exemplar Class 12 Maths Unit 7 Integrals.