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))