Evaluate the following Integrals:

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 cos2ϕ = 1-sin2ϕ

cos2ϕ = 1 – t2……(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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