Answer :

Given Definite Integral can be written as:

Let us assume sinϕ = t,

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

⇒ d(sinϕ) = d(t)

⇒ dt = cosϕ dϕ……(2)

Upper limit for the Definite Integral:

⇒ t = 1……(3)

Lower limit for the Definite Integral:

⇒ ϕ=0 ⇒ t = sin(0)

⇒ t = 0……(4)

We know that cos^{2}ϕ = 1-sin^{2}ϕ

⇒ cos^{2}ϕ = 1 – t^{2}……(5)

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

We know that:

We know that:

[here f’(x) is derivative of f(x))

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