Q. 225.0( 1 Vote )

Evaluate the following Integrals:


Answer :

Given Definite Integral can be written as:



We know that:








We know that: 1+tan2x = sec2x




Let us assume,


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





Upper limit for the Definite Integral:



y = 1+∞


y = ∞……(3)


Lower limit for the Definite Integral:


x = 0 y = 1+tan(0)


y = 1+0


y = 1……(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) = tan-1(∞) – tan-1(0)





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