**Class 12 maths NCERT Solutions Exercise 7.1-Integral**

**Class 12 maths NCERT Solutions Exercise 7.1 of Chapter 7-Integrals**-Here **NCERT solutions of class 12 maths exercise 7.1 of chapter 12** are the** solutions of** the **chapter 7 exercise 7.1-integrals of class maths NCERT** text book . All these **NCERT solutions** are well explained by the **maths** expert through a step by step method so that every student could be assessable to the** exercise 7.1 of chapter 7-Integral.** The purpose of these **NCERT Solutions of exercise 7.1** is to clear the concept of integration among the students of** class 12.**

**Class 12 maths NCERT Solutions Exercise 7.1-Integral**

Click for online shopping

**Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc**

**What is Integrals?** Integration is just opposite to differentiation,to understand integration let’s have a function (3x +2), its derivative is 3.Then we can say integral of 3 is 3x +C where C =2 is known as an arbitrary constant. It can be cleared by the following examples.

y = 3x, dy/dx=3

y =3x +2,dy/dx =3

y= 3x +3,dy/dx =3

The differentiation of yย with respect to x is the same 3, so we can say that integration of 3 isย 3x +C, where C may be any number, further, we can say that 3x +C is the indefinite integration(integral) of 3 , in other words, it can also be called that 3x+C is the anti-derivative of 3.

If there is a function f(x) such that its derivative is g(x),then f(x) is anti-derivative(Integral) of the function g(x).Therefore when the differentiation of a function is integrated we get the original function,in simple words integration is opposite of diffrentiation.

The d/dx(x^{n}) = nx^{n-1}

Here, integral of nx^{n-1 }is x^{n}

**Integration** is represented by the sign **โซ** and dx is attached at the end of the function which means integration of the function with respect to x. The integral of a function is calculated as follows.

Application of integration: When differentiated parts of a region within limits combine together we get the integral of the function within the region. So, integration is used to calculate physical quantities like area, volume, mass, etc.It is widely used in science and technology for the evaluation of the different type of physical quantities and in business predicting the outcomes of particular inputs applied.

**Class 12 Maths NCERT solutions of Chapter 7 Integrals**

**NCERT Solutions Exercise 7.1-Integral**

**Q1.Find an anti-derivative (or integral) of the following functions by the method of inspection**

**Sin 2x**

Ans.

We know -sinฮธ is the derivative of cosฮธ,so differentiation of cosฮธ is =-sin

Hence anti-derivative of sin2x is -1/2(cos2x).

**Q2.Find an anti-derivative (or integral) of the following functions by the method of inspection**

**cos 3x**

Ans. We know cosฮธ is the derivative of sinฮธ

Therefore anti-derivative (integral) of cos3x is 1/3(sin3x).

**Best deals in Amazon**

**Q3.Find an anti-derivative (or integral) of the following functions by the method of inspection**

Ans.We know the derivative of is ,so

Therefore anti-derivative of is 1/2().

**Q4.Find an anti-derivative (or integral) of the following functions by the method of inspection**

**(ax +b)ยฒ**

Ans.We know the derivative of xยณ is 3xยฒ, so

Therefore antiderivative of (ax+b)ยฒ is 1/3a(ax+b)ยณ

**Class 12 Maths NCERT solutions of Chapter 7 Integrals**

**Q5.Find an anti-derivative (or integral) of the following functions by the method of inspection**

Ans.We know -sinฮธ is the derivative of cosฮธ

We know derivative ofย is

Subtracting equation (ii) from (i), we get

Therefore antiderivative of ย isย ย

Find the following integrals from Exercises 6ย to 20.

**Q6.**

Ans.

Ans.

Ans.

**Class 12 Maths NCERT solutions of Chapter 7 Integrals**

Ans.

Ans.

Writting the function in expanded form

Ans.

Ans.

**Class 12 Maths NCERT solutions of Chapter 7 Integrals**

Ans.

Dividingย numerator by the denominator, we get xยฒ +1

Ans.

+ C

Ans.

+ C

Ans.

Ans.

Ans. On multiplication, we get,

By taking separately, we get,

We get,

= tan x + sec x + C

Ans. We get,

So,

We get,

On further calculation, we get,

By taking seriously, we get

= tan x – x + C

**Class 12 Maths NCERT solutions of Chapter 7 Integrals**

Ans.

Ans.

Therefore the correct answer is (C)

Ans. We are given

Therefore anti-derivative ofย ย ย is f(x)

We are given f(2) =0

Substituting this value of C in f(x)

Therefore the correct answer is (A)

You can compensate us

**Paytm number 9891436286**

The money collected by us will be used for the education of poor students who leaves their study because of a lack of money.

**NCERT Solutions of Science and Maths for Class 9,10,11 and 12**

**NCERT Solutions for class 9 maths**

**NCERT Solutions for class 9 scienceย **

**NCERT Solutions for class 10 maths**

**CBSE Class 10-Question paper of maths 2021 with solutions**

**CBSE Class 10-Half yearly question paper of maths 2020 with solutions**

**CBSE Class 10 -Question paper of maths 2020 with solutions**

**CBSE Class 10-Question paper of maths 2019 with solutions**

**NCERT Solutions for Class 10 Science**

**NCERT Solutions for class 11 maths**

Chapter 1-Sets | Chapter 9-Sequences and Series |

Chapter 2- Relations and functions | Chapter 10- Straight Lines |

Chapter 3- Trigonometry | Chapter 11-Conic Sections |

Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |

Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |

Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |

Chapter 7- Permutations and Combinations | Chapter 15- Statistics |

Chapter 8- Binomial Theorem | ย Chapter 16- Probability |

**CBSE Class 11-Question paper of maths 2015**

**CBSE Class 11 – Second unit test of maths 2021 with solutions**

**NCERT solutions for class 12 maths**

Chapter 1-Relations and Functions | Chapter 9-Differential Equations |

Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |

Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |

Chapter 4-Determinants | Chapter 12-Linear Programming |

Chapter 5- Continuity and Differentiability | Chapter 13-Probability |

Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |

Chapter 7- Integrals | |

Chapter 8-Application of Integrals |

**Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2**

**Class 12 Maths Important Questions-Application of Integrals**

**Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22**

**Solutions of class 12ย maths question paper 2021 preboard exam CBSE Solution**