Evaluate the following integral:

Let us assume .....……equation 1

Let

thus

Differentiating both sides, we get,

Thus substituting old limits, we get a new upper limit and lower limit

For a = a cos θ

0 = θ

For 0 = acos θ

We know that

thus

Substituting the values in equation 1

We know that

Trigonometric identity 1 – cos² θ = sin² θ

.......equation 2

By property, we know that

thus

.........equation 3

Adding equation 3 and equation 2

Thus

We know

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