Q. 115.0( 2 Votes )

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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 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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