Evaluate the following Integrals:
Given Definite Integral can be written as:
……(1)
We know that:
And
Let us find the value of 5cosx+3sinx
We know that: 1+tan2x = sec2x
……(2)
Substituting (2) in (1) we get,
Let us assume:
Differentiating on both sides w.r.t x we get,
……(3)
The upper limit for the Definite Integral:
⇒ t=1……(4)
The lower limit for the Definite Integral:
⇒ t=0……(5)
Substituting (3),(4),(5) in the eq(1) we get,
We need to convert the denominator into standard forms
We know that:
In this problem the values,
Using these values and the standard result, we get,
We know that:
[here f’(x) is derivative of f(x))
We know that: