Evaluate the following Integrals:

Given Definite Integral can be written as:


……(1)


Let us assume y = x2


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


d(y) = d(x2)


dy = 2xdx……(2)


Lower limit for the Definite Integral:


x = 0 y = 02


y = 0……(3)


Upper limit for the Definite Integral:


x = 1 y = 12


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(1) – tan-1(0)





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