Evaluate the following Integrals:
Let
Put x = sin θ
⇒ dx = cos θ dθ (Differentiating both sides)
Also,
When x = 0, sin θ = 0 ⇒ θ = 0
So, the new limits are 0 and.
Substituting this in the original integral,
Dividing numerator and denominator with cos2θ, we have
[∵ sec2θ = 1 + tan2θ]
Put tan θ = t
⇒ sec2θ dθ = dt (Differentiating both sides)
When θ = 0, t = tan 0 = 0
So, the new limits are 0 and.
Substituting this in the original integral,
Recall