Evaluate the following integral:

Let us assume .....….equation 1

By property, we know that

thus

.....………….equation 2

Since

Adding equation 1 and equation 2

We know

Thus

Adding and subtracting 1

)

We know

)

Let

Let

.......equation 3

Solving I₁:

We know b and a being the upper and lower limits respectively.

Solving I2:

Using trigonometric identity and formula

Taking common

Let

Differentiating both sides, we get,

For x = 0

For x = π

Substituting the values

Thus

We know b and a being the upper and lower limits respectively

Substituting values in equation 3