Evaluate the following Integrals:

Given Definite Integral can be written as:

Let us assume 1+cosθ=y

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

⇒ d(1+cosθ) = d(y)

⇒ -sinθdθ = dy

⇒ sinθdθ = -dy……(2)

Upper limit for the Definite Integral

⇒ y = 1……(3)

Lower limit for the Definite Integral:

⇒ θ = 0 ⇒ y = 1+cos(0)

⇒ y = 1+1

⇒ y = 2……(4)

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

We know that:

We know that:

We know that:

[here f’(x) is derivative of f(x))