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)

Upper limit for the Definite Integral:

⇒ x = 1 ⇒ y = 1²

⇒ y = 1 ……(3)

Lower limit for the Definite Integral:

⇒ x = 0 ⇒ y = 0²

⇒ y = 0 ……(4)

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

We know that: ∫ e^xdx = e^x+c

We know that:

[here f’(x) is derivative of f(x))