Evaluate the following Integrals:

Given Definite Integral can be written as:

Let us assume, y = sin²x

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

⇒ d(y) = d(sin²x)

⇒ dy = 2sinxcosxdx

Upper limit for the Definite Integral:

⇒ y = 1…… (3)

Lower limit for the Definite Integral:

⇒ x = 0 ⇒ y = sin²0

⇒ y = 0……(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))