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=