Q. 55.0( 1 Vote )

# Evaluate the following Integrals:

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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