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)