# Class 12 Maths NCERT Solutions of exercise 7.3 of the chapter 7-Integrals

**Class 12 Maths NCERT solutions of exercise 7.3 of the chapter 7-Integrals** are the **solutions of exercise 7.3 of the chapter 7-Integrals of class 12 NCERT maths** textbook. **Class 12 Maths NCERT Solutions of exercise 7.3 of the chapter 7-Integrals** are compulsory to be studied for every** maths** student of** class 12** for clearing the concept of the methods used for solving the questions based on the** integration** of the functions. In this **exercise 7.3,** you will study the** integration** of different types of complex trigonometric functions. The **solutions of exercise 7.3** are required the inputs of class 11 chapter 3- trigonometric functions because for simplification of complex trigonometric functions the trigonometric identities are required to use for the integration of the functions.

As an example, we can not integrate the function directly Cos²2x, so using the trigometric identity cosA = 2cos²A – 1⇒ cos²A = (1+cosA)/2, so cos²2x = (1+cos4x)/2

Now, integrating the simplified function ((1+cos4x)/2), we have

1/2∫(1+cos4x)dx = 1/2[∫1dx +∫cos4xdx] = x/2 +(1/2)(sin4x)/4 +C= x/4 + (1/8)sin4x +C

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

**Class 12 Maths NCERT Solutions of exercise 7.3 **

**Q1.Integrate sin²(2x +5)**

Ans.We are given the function

sin²(2x +5)

Applying the trigonometric identity

cos2A=1 – 2sin²A

Now, integrating it

Integrating each terms individually

**Q2.Integrate sin3x cos4x.**

Using the trigonometric identity

2sinAcosB = sin(A+B)+ sin (A-B)

Now, integrating it

Integrating each term individually

**Q3.Integrate cos2x cos4x cos6x**

Ans. We are given the function

cos2x cos4x cos6x

Using the trigonometric identity

Now, integrating the given function

Again,applying the identities cos²2x= (1 + cos4x)/2 and

**Q4.Integrate sin³(2x +1)**

Ans. We are given the function

sin³(2x +1)

Integrating the function

Rewriting the given function

Applying the trigonometric identity

sin²(2x+1) = 1 – cos²(2x+1)

Using the substitution method

Let t = cos(2x+1)

Substituting cos(2x+1) =t and sin(2x+1)dx=-dt/2

Now,substituting back the value of t= cos(2x+1)

**Q5.cos³xsin³x**

Ans. We are given

cos³xsin³x

Integrating it

Using the identy sin²x = 1-cos²x

Let t= cosx

-dt = sinx dx

Substituting cosx and sinxdx by t and -dt respectively

Substituting back the value of t= cosx

**Q6.sinx sin 2x sin3x**

Ans.We are given the function

sinx sin 2x sin3x

Integrating it

Using the trigonometric identity

Using cos(-x) = cosx

Substituting the value of sin2x sin3x

Using the identity 2sinx cosx = sin2x, and sinx cos5x = 1/2[sin(x+5x) +sin(x-5x)], we get

Using sin(x-5x) = sin(-4x) = -sin4x

### Class 12 Maths NCERT Solutions of exercise 7.3 of the chapter 7-Integrals

**Q7.Integrate sin4x sin8x**

Ans. We are given

sin4x sin8x

Integrating it

Using the trigonometric identity

sinA.sinB = 1/2(cos(A-B) -cos(A+B)

**Q8. Integrate**

Ans. We are given

Applying the identity 1-cosx = 2sin²x/2 and 1+cox = 2cos²x/2

Also applying tan²x/2 =sec²x/2 – 1

Now, integrating it

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

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

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

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