**Class 12 Maths NCERT Solutions of exercise 7.3 -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

**NCERT solutions of exercise 7.2-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

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

The solutions of 8 questions of the chapter 7 of exercise 7.3 are for clearing your concept of the method used in the exercise 7.3-Integrals, solutions of rest of the questions you can find here within 3 days, till then study other chapters of NCERT maths text book of class 12,links are given bellow.

**You can also study NCERT solutions Class 12 Maths**

**Exercise 6.1-Application of Derivatives**

**Exercise 6.2-Application of Derivatives**

**Exercise 6.3 -Application of Derivatives**

**Exercise 6.4- Application of Derivatives**

** Exercise 6.5-Application of Derivations**

**Exercise 5.2 Chapter- Continuity and Differentiability**

**Chapter 5-Continuity and Differentiability**

**Chapter 1- Relations and functions-Download free pdf**

**Class 11 NCERT solutions Chapter 1 of maths, physics and chemistry**

**Chapter 1-Sets(important questions)**

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