Evaluate the following Integrals:
Let
We have sin2x + cos2x = 1 and sec2x – tan2x = 1
We can write sin3x = sin2x × sin x = (1 – cos2x) sin x
Put cos x = t
⇒ –sin(x)dx = dt (Differentiating both sides)
⇒ sin(x)dx = –dt
When x = 0, t = cos 0 = 1
So, the new limits are 1 and 0.
Substituting this in the original integral,
Recall