Given Definite Integral can be written as:

…… (1)

Let us assume x = a sinθ

Differentiating w.r.t x on both sides we get,

⇒ d(x) = d(a sin θ)

⇒ dx = a cos θ dθ ……(2)

Let us find the value of

(∵ 1 – sin²θ = cos²θ)

……(3)

Lower limit for the Definite Integral:

⇒ θ = sin^-1(0)

⇒ θ = 0……(4)

Upper limit for the Definite Integral:

⇒ θ = sin^-1(1)

……(5)

Substituting (2),(3),(4),(5) in eq(1) we get,

We know that cos2θ = 2cos²θ – 1

Then

Using these result for the integration, we get,

We know that:

∫ adx = ax + c and also

We know that:

[here f’(x) is derivative of f(x)).

We know that sinnπ = 0 (n∈I)