Class 12 RD Sharma Solutions- Chapter 19 Indefinite Integrals - Exercise 19.7

Integrate the following integrals:

Question 1. ∫sin4x cos7x dx

Solution:

Let I= 

We know,

Applying this formula to the given question we get

I=

= 

=

=

We know,

Applying this formula to the given question we get

I= 

 I= 

Question 2. ∫ cos3x cos4x dx

Solution:

Let I= 

Multiplying and dividing the equation by 2,we get

I=

We know,

Applying this formula to the given question we get

I=

=

We know,

  and 

Applying these formulas to the given question we get

I=

 I=

Question 3. ∫ cosmx cosnx dx, m≠​n

Solution:

Let I= 

Multiplying and dividing the equation by 2,we get

I=

We know,

Applying this formula to the given question we get

I=

We know,

Applying these formulas to the given question we get

 I=

Question 4. ∫ sinmx cosnx dx, m≠n

Solution:

Let I=

Multiplying and dividing the equation by 2,we get

I=

We know,

Applying this formula to the given question we get

I=

We know,

Applying these formulas to the given question we get

 I= 

Summary

This exercise in Chapter 19 Indefinite Integrals focuses on evaluating a variety of indefinite integrals using different integration techniques. The practice questions cover a wide range of functions, including polynomials, trigonometric functions, exponential functions, and rational functions.

Students will need to apply methods such as the power rule, integration by parts, substitution, and integration of trigonometric and rational functions to solve these problems. The aim is to help students develop proficiency in applying various integration techniques and strengthen their understanding of indefinite integrals.

The problems range in complexity, starting with simpler polynomial and trigonometric integrals, and progressing to more challenging integrals involving exponential and rational functions. Solving these practice questions will equip students with the skills to tackle a diverse set of indefinite integral problems.