Evaluate the following integral:
let us assume
let x = tany
differentiating both sides
dx = sec2 y dy
for x = ∞
For x = 0
0 = y
thus
(since sec2y – tan2y = 1)
.....equation 1
By property, we know that
….....equation 2
Adding equations 1 and 2, we get,
We know
since logm + logn = logmn
since tany = 1/coty
since log 1 = 0
Thus
2I = 0
I = 0