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.