Evaluate the following Integrals:

Given Definite Integral can be written as:

We know that:

Substituting in the Definite Integral we get,

Let us assume, y = sinx – cosx

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

⇒ d(y) = d(sinx – cosx)

⇒ dy = (cosx + sinx)dx……(2)

Upper limit for the Definite Integral:

⇒ y = 0…… (3)

Lower limit for the Definite Integral:

⇒ x = 0 ⇒ y = sin(0) – cos(0)

⇒ y = 0 – 1

⇒ 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))