Q. 55.0( 1 Vote )

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Answer :

Given Definite integral can be written as:


(1)


Let us assume y = a2+x2


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


d(y) = d(a2+x2)


dy = 2xdx


……(2)


Upper limit for the Definite Integral:


x=a y = a2+a2


y=2a2……(3)


Lower limit for the Definite Integral:


x=0 y = a2+02


y = a2……(4)


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




We know that:





We know that:


[here f’(x) is derivative of f(x))


I(x) = (2a2 )1/2 – (a2 )1/2


I(x) = √2 a – a


I(x) = a(√2–1)



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