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

### Question 1. âˆ«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. âˆ« 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. âˆ«cosmx cosnx dx, mâ‰ â€‹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. âˆ« sinmx cosnx dx, mâ‰ 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=

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