Let

Put 5 – 4 cos θ = x

⇒ 4sin(θ)dθ = dx (Differentiating both sides)

When θ = 0, x = 5 – 4 cos 0 = 5 – 4 = 1

When θ = π, x = 5 – 4 cos π = 5 – (–4) = 9

So, the new limits are 1 and 9.

Substituting this in the original integral,

Recall