Q. 105.0( 1 Vote )

# Evaluate the integral Ideas required to solve the problems:

* Integration by substitution: A change in the variable of integration often reduces an integral to one of the fundamental integration. If derivative of a function is present in an integration or if chances of its presence after few modification is possible then we apply integration by substitution method.

* Knowledge of integration of fundamental functions like sin, cos ,polynomial, log etc and formula for some special functions.

Let, I = To solve such integrals involving trigonometric terms in numerator and denominators. We use the basic substitution method and to apply this simply we follow the undermentioned procedure-

If I has the form Then substitute numerator as - Where A, B and C are constants

We have, I = As I matches with the form described above, So we will take the steps as described.  {  Comparing both sides we have:

C = 0

2B - 3A = 1

3B + 2A = 8

On solving for A ,B and C we have:

A = 1 , B = 2 and C = 0

Thus I can be expressed as:

I = I = Let I1 = and I2 = I = I1 + I2 ….equation 1

I1 = Let, 3 cos x + 2 sin x = u

(-3sin x + 2cos x)dx = du

So, I1 reduces to:

I1 = I1 = …..equation 2

As, I2 = I2 = …..equation 3

From equation 1, 2 and 3 we have:

I = I = Rate this question :

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